Problem 9
Question
Find the determinant of the matrix. $$\left[\begin{array}{rr} -7 & 6 \\ \frac{1}{2} & 3 \end{array}\right]$$
Step-by-Step Solution
Verified Answer
The determinant of the matrix is -24.
1Step 1: Identify Matrix Elements
Firstly, identify the elements of the matrix \(\left[\begin{array}{rr}-7 & 6 \ rac{1}{2} & 3\end{array}\right]\). They correspond to \[a = -7\], \[b = 6\], \[c = \frac{1}{2}\] and \[d = 3\].
2Step 2: Apply the Formula
Then use the determinant formula for 2x2 matrix, which is \[|A| = a*d - b*c\]. Substituting given values: \[|A| = -7*3 - 6*\frac{1}{2}\].
3Step 3: Calculate Result
Do the multiplications and subtraction: |-21 - 3|= -24.
Other exercises in this chapter
Problem 8
What is the dimension of \(A B\) when \(A\) is a \(2 \times 3\) matrix and \(B\) is a \(3 \times 4\) matrix?
View solution Problem 8
Is a consistent system with infinitely many solutions independent or dependent?
View solution Problem 9
The Inverse of a Matrix, show that \(B\) is the inverse of \(A\). $$A=\left[\begin{array}{rrr} 2 & -17 & 11 \\ -1 & 11 & -7 \\ 0 & 3 & -2 \end{array}\right], \q
View solution Problem 9
Determine the dimension of the matrix. $$\left[\begin{array}{r} 4 \\ 32 \\ 3 \end{array}\right]$$
View solution