Chapter 10

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{lll}1 & 0 & 2 \\\3 & 1 & 0 \\\1 & 2 & 1\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &2 x+y=11\\\ &3 x-y=4 \end{aligned}$$

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{rr}3 & 2 \\ 1 & -4\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrr}2 & -1 & 3 \\\0 & 2 & 1 \\\3 & -2 & 4\end{array}\right|$$

Given the following arrays: A=\(\left(\begin{array}{lll}2 & 5 & 1 \\ 6 & 3 & 7 \\ 1 & 6 & 9 \\ 7 & 4 & 2\end{array}\right)\) B=\(\left(\begin{array}{l}7 \\ 3 \\ 9 \\ 2\end{array}\right)\) C=\(\left(\begin{array}{cccc}f & i & q & w \\ & g & w & k \\ & & c & z \\ & & & b\end{array}\right)\) D=\(\left(\begin{array}{llll}6 & 2 & 0 & 1 \\ 2 & 8 & 3 & 9\end{array}\right)\) E=\(\left(\begin{array}{ll}x & y \\ z & w\end{array}\right)\) F=\(\left(\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right)\) G=7 H=\(\left(\begin{array}{cc}3 & 8 \\ & 5\end{array}\right)\) I=\(\left(\begin{array}{llll}3 & 8 & 4 & 6\end{array}\right)\) J=\(\left(\begin{array}{llll}3 & 7 & 2 & 1 \\ 5 & 2 & 9 & 3 \\ 5 & 1 & 7 & 2 \\\ 7 & 3 & 9 & 1\end{array}\right)\) K=\(\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1\end{array}\right)\) Which of the 11 arrays shown is a square array?

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &5 x+7 y=101\\\ &7 x-y=55 \end{aligned}$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrr}-3 & 1 & 2 \\\0 & -1 & 5 \\\6 & 0 & 1\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &3 x-2 y=-15\\\ &5 x+6 y=3 \end{aligned}$$

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{rr}0 & 5 \\ -3 & -4\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrr}-1 & 0 & 3 \\\2 & 0 & -2 \\\1 & -3 & 4\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &7 x+6 y=20\\\ &2 x+5 y=9 \end{aligned}$$

A=\(\left(\begin{array}{lll}2 & 5 & 1 \\ 6 & 3 & 7 \\ 1 & 6 & 9 \\ 7 & 4 & 2\end{array}\right)\) B=\(\left(\begin{array}{l}7 \\ 3 \\ 9 \\ 2\end{array}\right)\) C=\(\left(\begin{array}{cccc}f & i & q & w \\ & g & w & k \\ & & c & z \\ & & & b\end{array}\right)\) D=\(\left(\begin{array}{llll}6 & 2 & 0 & 1 \\ 2 & 8 & 3 & 9\end{array}\right)\) E=\(\left(\begin{array}{ll}x & y \\ z & w\end{array}\right)\) F=\(\left(\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right)\) G=7 H=\(\left(\begin{array}{cc}3 & 8 \\ & 5\end{array}\right)\) I=\(\left(\begin{array}{llll}3 & 8 & 4 & 6\end{array}\right)\) J=\(\left(\begin{array}{llll}3 & 7 & 2 & 1 \\ 5 & 2 & 9 & 3 \\ 5 & 1 & 7 & 2 \\\ 7 & 3 & 9 & 1\end{array}\right)\) K=\(\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1\end{array}\right)\) Which of the 11 arrays shown is a column vector?

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{rr}8 & 3 \\ -1 & 2\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrr}5 & 1 & 2 \\\\-3 & 2 & -1 \\\4 & -3 & 5\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{array}{r} x+5 y=11 \\ 3 x+2 y=7 \end{array}$$

A=\(\left(\begin{array}{lll}2 & 5 & 1 \\ 6 & 3 & 7 \\ 1 & 6 & 9 \\ 7 & 4 & 2\end{array}\right)\) B=\(\left(\begin{array}{l}7 \\ 3 \\ 9 \\ 2\end{array}\right)\) C=\(\left(\begin{array}{cccc}f & i & q & w \\ & g & w & k \\ & & c & z \\ & & & b\end{array}\right)\) D=\(\left(\begin{array}{llll}6 & 2 & 0 & 1 \\ 2 & 8 & 3 & 9\end{array}\right)\) E=\(\left(\begin{array}{ll}x & y \\ z & w\end{array}\right)\) F=\(\left(\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right)\) G=7 H=\(\left(\begin{array}{cc}3 & 8 \\ & 5\end{array}\right)\) I=\(\left(\begin{array}{llll}3 & 8 & 4 & 6\end{array}\right)\) J=\(\left(\begin{array}{llll}3 & 7 & 2 & 1 \\ 5 & 2 & 9 & 3 \\ 5 & 1 & 7 & 2 \\\ 7 & 3 & 9 & 1\end{array}\right)\) K=\(\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1\end{array}\right)\) Which of the 11 arrays shown is a row vector?

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{rr}-4 & 5 \\ 7 & -2\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrr}1.0 & 2.4 & -1.5 \\\\-2.6 & 0 & 3.2 \\\\-2.9 & 1.0 & 4.1\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &4 x-5 y=-34\\\ &2 x-3 y=-22 \end{aligned}$$

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{rr}7 & -6 \\ -5 & 4\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrr}2 & 1 & 3 \\\0 & -2 & 4 \\\0 & 1 & 5\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{array}{r} x+4 y=11 \\ 5 x-2 y=11 \end{array}$$

A=\(\left(\begin{array}{lll}2 & 5 & 1 \\ 6 & 3 & 7 \\ 1 & 6 & 9 \\ 7 & 4 & 2\end{array}\right)\) B=\(\left(\begin{array}{l}7 \\ 3 \\ 9 \\ 2\end{array}\right)\) C=\(\left(\begin{array}{cccc}f & i & q & w \\ & g & w & k \\ & & c & z \\ & & & b\end{array}\right)\) D=\(\left(\begin{array}{llll}6 & 2 & 0 & 1 \\ 2 & 8 & 3 & 9\end{array}\right)\) E=\(\left(\begin{array}{ll}x & y \\ z & w\end{array}\right)\) F=\(\left(\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right)\) G=7 H=\(\left(\begin{array}{cc}3 & 8 \\ & 5\end{array}\right)\) I=\(\left(\begin{array}{llll}3 & 8 & 4 & 6\end{array}\right)\) J=\(\left(\begin{array}{llll}3 & 7 & 2 & 1 \\ 5 & 2 & 9 & 3 \\ 5 & 1 & 7 & 2 \\\ 7 & 3 & 9 & 1\end{array}\right)\) K=\(\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1\end{array}\right)\) Which of the 11 arrays shown is a list?

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{cc}4.82 & 2.73 \\ 2.97 & 5.28\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrr}1 & 5 & 4 \\\\-3 & 6 & -2 \\\\-1 & 5 & 3\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &2 x-3 y=3\\\ &4 x+5 y=39 \end{aligned}$$

A=\(\left(\begin{array}{lll}2 & 5 & 1 \\ 6 & 3 & 7 \\ 1 & 6 & 9 \\ 7 & 4 & 2\end{array}\right)\) B=\(\left(\begin{array}{l}7 \\ 3 \\ 9 \\ 2\end{array}\right)\) C=\(\left(\begin{array}{cccc}f & i & q & w \\ & g & w & k \\ & & c & z \\ & & & b\end{array}\right)\) D=\(\left(\begin{array}{llll}6 & 2 & 0 & 1 \\ 2 & 8 & 3 & 9\end{array}\right)\) E=\(\left(\begin{array}{ll}x & y \\ z & w\end{array}\right)\) F=\(\left(\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right)\) G=7 H=\(\left(\begin{array}{cc}3 & 8 \\ & 5\end{array}\right)\) I=\(\left(\begin{array}{llll}3 & 8 & 4 & 6\end{array}\right)\) J=\(\left(\begin{array}{llll}3 & 7 & 2 & 1 \\ 5 & 2 & 9 & 3 \\ 5 & 1 & 7 & 2 \\\ 7 & 3 & 9 & 1\end{array}\right)\) K=\(\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1\end{array}\right)\) Which of the 11 arrays shown is a scalar?

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{rr}48.7 & -53.6 \\ 4.93 & 9.27\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrrr}4 & 3 & 1 & 0 \\\\-1 & 2 & -3 & 5 \\\0 & 1 & -1 & 2 \\\0 & 2 & -3 & 5\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &7 x-4 y=81\\\ &5 x-3 y=57 \end{aligned}$$

A=\(\left(\begin{array}{lll}2 & 5 & 1 \\ 6 & 3 & 7 \\ 1 & 6 & 9 \\ 7 & 4 & 2\end{array}\right)\) B=\(\left(\begin{array}{l}7 \\ 3 \\ 9 \\ 2\end{array}\right)\) C=\(\left(\begin{array}{cccc}f & i & q & w \\ & g & w & k \\ & & c & z \\ & & & b\end{array}\right)\) D=\(\left(\begin{array}{llll}6 & 2 & 0 & 1 \\ 2 & 8 & 3 & 9\end{array}\right)\) E=\(\left(\begin{array}{ll}x & y \\ z & w\end{array}\right)\) F=\(\left(\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right)\) G=7 H=\(\left(\begin{array}{cc}3 & 8 \\ & 5\end{array}\right)\) I=\(\left(\begin{array}{llll}3 & 8 & 4 & 6\end{array}\right)\) J=\(\left(\begin{array}{llll}3 & 7 & 2 & 1 \\ 5 & 2 & 9 & 3 \\ 5 & 1 & 7 & 2 \\\ 7 & 3 & 9 & 1\end{array}\right)\) K=\(\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1\end{array}\right)\) Which of the 11 arrays shown is a null matrix?

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{cc}-2 / 3 & 2 / 5 \\ -1 / 3 & 4 / 5\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrrr}-1 & 3 & 0 & 2 \\\2 & -1 & 1 & 0 \\\5 & 2 & -2 & 0 \\\1 & -1 & 3 & 1\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &3 x+4 y=85\\\ &5 x+4 y=107 \end{aligned}$$

A=\(\left(\begin{array}{lll}2 & 5 & 1 \\ 6 & 3 & 7 \\ 1 & 6 & 9 \\ 7 & 4 & 2\end{array}\right)\) B=\(\left(\begin{array}{l}7 \\ 3 \\ 9 \\ 2\end{array}\right)\) C=\(\left(\begin{array}{cccc}f & i & q & w \\ & g & w & k \\ & & c & z \\ & & & b\end{array}\right)\) D=\(\left(\begin{array}{llll}6 & 2 & 0 & 1 \\ 2 & 8 & 3 & 9\end{array}\right)\) E=\(\left(\begin{array}{ll}x & y \\ z & w\end{array}\right)\) F=\(\left(\begin{array}{llll}0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{array}\right)\) G=7 H=\(\left(\begin{array}{cc}3 & 8 \\ & 5\end{array}\right)\) I=\(\left(\begin{array}{llll}3 & 8 & 4 & 6\end{array}\right)\) J=\(\left(\begin{array}{llll}3 & 7 & 2 & 1 \\ 5 & 2 & 9 & 3 \\ 5 & 1 & 7 & 2 \\\ 7 & 3 & 9 & 1\end{array}\right)\) K=\(\left(\begin{array}{llll}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1\end{array}\right)\) Which of the 11 arrays shown is a unit matrix?

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{rr}1 / 2 & 1 / 4 \\ -1 / 2 & -1 / 4\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrrr}2 & 0 & -1 & 0 \\\0 & 0 & 2 & -1 \\\1 & 3 & 2 & 1 \\\3 & 1 & 1 & -2\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &3 x-2 y=1\\\ &2 x+y=10 \end{aligned}$$

For matrix \(\mathbf{A},\) find each of the following elements: $$a_{32}$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{rrrr}1 & 2 & -1 & 1 \\\\-1 & 1 & 2 & 3 \\\3 & -1 & 1 & 2 \\\1 & 2 & -1 & 1\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &5 x-2 y=3\\\ &2 x+3 y=5 \end{aligned}$$

Find the value of each determinant. Do and/or check some by calculator. $$\left|\begin{array}{cc}2 m & 3 n \\ -m & 4 n\end{array}\right|$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{lllll}3 & 1 & 0 & 2 & 4 \\\1 & 2 & 4 & 0 & 1 \\\2 & 3 & 1 & 4 & 2 \\\1 & 2 & 0 & 2 & 1 \\\3 & 4 & 1 & 3 & 1\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &y=9-3 x\\\ &x=8-2 y \end{aligned}$$

Solve by determinants. $$\begin{array}{l} 4 x+2 y=3 \\ -4 x+y=6 \end{array}$$

Evaluate determinant by calculator or by minors. $$\left|\begin{array}{lllll}2 & 1 & 5 & 3 & 6 \\\1 & 4 & 2 & 4 & 3 \\\3 & 1 & 2 & 4 & 1 \\\5 & 2 & 3 & 1 & 4 \\\4 & 5 & 2 & 3 & 1\end{array}\right|$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{aligned} &y=2 x-3\\\ &x=19-3 y \end{aligned}$$

Solve by determinants. $$\begin{aligned} &2 x-3 y=5\\\ &3 x+3 y=10 \end{aligned}$$

Solve by determinants. Evaluate the determinants by calculator or by minors. $$\begin{aligned}&x+y+z=18\\\&x-y+z=6\\\&x+y-z=4\end{aligned}$$

Solve each system of equations by calculator using the unit matrix method. Two Equations in Two Unknowns. $$\begin{array}{l} 29.1 x-47.6 y=42.8 \\ 11.5 x+72.7 y=25.8 \end{array}$$