Q 4.92 - Intermediate Algebra

Question

For the determinant $\left[\begin{array}{ccc}-2& -1& 0\\ 3& 0& -1\\ -1& -2& 3\end{array}\right]$, find and then evaluate the minor of (a) a₂ (b) b₃ (c) c2 

Step-by-Step Solution

Answer

The minor of a₂=-3

The minor of b₃=2

The minor of c₂=3

Step 1. Given information

The given determinant is $\left[\begin{array}{ccc}-2& -1& 0\\ 3& 0& -1\\ -1& -2& 3\end{array}\right]$

Step 2. Calculation

(a) Eliminate the row and column that contains a2. 

and write 2*2 determinant that remains

$$\begin{gathered} \mathrm{minor} \mathrm{of} a_2=\left|\begin{array}{cc}-1& 0\\ -2& 3\end{array}\right| \\ \mathrm{by} \mathrm{evaluating} = (-1\times 3)-(0\times -2) \\ =-3+0 \\ =-3 \end{gathered}$$

(b) Eliminate the row and column that contains b3. 

and write 2*2 determinant that remains

$$\begin{gathered} \mathrm{minor} \mathrm{of} b_3=\left|\begin{array}{cc}-2& 0\\ 3& -1\end{array}\right| \\ \mathrm{by} \mathrm{evaluating} = (-1\times -2)-(0\times 3) \\ =2 \end{gathered}$$

(c) Eliminate the row and column that contains c2. 

and write 2*2 determinant that remains

$$\begin{gathered} \mathrm{minor} \mathrm{of} c_2=\left|\begin{array}{cc}-2& -1\\ -1& -2\end{array}\right| \\ \mathrm{by} \mathrm{evaluating} = (-2\times -2)-(-1\times -1) \\ =4-\left(1\right) \\ =3 \end{gathered}$$