Evaluate the determinant of the given matrix and state whether the matrix is invertible.
-$$A = \left[ \begin{array} { r r r r }
7 & 0 & 2 & - 7 \
- 3 & - 4 & 9 & 5 \
0 & - 1 & 6 & 5 \
9 & 5 & 6 & 2
\end{array} \right]$$
A) 648 , No
B) $648 , \mathrm { Yes }$
C) $1,026 , \mathrm { Yes }$
D) $1,026 , \mathrm { No }$

Question

Evaluate the determinant of the given matrix and state whether the matrix is invertible.
-$$A = \left[ \begin{array} { r r r r } 
7 & 0 & 2 & - 7 \
- 3 & - 4 & 9 & 5 \
0 & - 1 & 6 & 5 \
9 & 5 & 6 & 2
\end{array} \right]$$
A) 648 , No
B) $648 , \mathrm { Yes }$
C) $1,026 , \mathrm { Yes }$
D) $1,026 , \mathrm { No }$

Quizplus · Accepted Answer

The determinant of matrix A can be calculated using various methods such as Laplace's expansion, row reduction, or leveraging properties of determinants. The determinant of A is 648. A matrix is invertible if and only if its determinant is not equal to zero. Since the determinant of A is 648 (which is not equal to zero), the matrix is invertible.

Evaluate the Determinant of the Given Matrix and State Whether A=[702−7−3−4950−1659562]A = \left[ \begin{array} { r r r r } 7 & 0 & 2 & - 7 \\- 3 & - 4 & 9 & 5 \\0 & - 1 & 6 & 5 \\9 & 5 & 6 & 2\end{array} \right]A=​7−309​0−4−15​2966​−7552​​

Evaluate the Determinant of the Given Matrix and State Whether $A = \left[ \begin{array} { r r r r } 7 & 0 & 2 & - 7 \\- 3 & - 4 & 9 & 5 \\0 & - 1 & 6 & 5 \\9 & 5 & 6 & 2\end{array} \right]$