QUESTION 7.2 How do I know a matrix is Invertible Choose one $\cdot 4$ points Why is $A=\left(\begin{array}{ll}1 & 4 \\ 1 & 3\end{array}\right)$ invertible? Because $\operatorname{det}(A)=0$ Because $\operatorname{det}(A) \neq 0$ Because $A=0$
Solution
Step 1 ：The determinant of a matrix is a special number that can be calculated from a square matrix. A Matrix is Invertible if and only if its determinant is not equal to zero.
Step 2 ：To find out if the given matrix A is invertible, we need to calculate its determinant and check if it is not equal to zero.
Step 3 ：The given matrix A is \(A=\left(\begin{array}{ll}1 & 4 \\ 1 & 3\end{array}\right)\).
Step 4 ：Calculate the determinant of matrix A, \(\operatorname{det}(A)\).
Step 5 ：The determinant of matrix A is -1, which is not equal to zero.
Step 6 ：\(\boxed{\text{Therefore, the matrix } A=\left(\begin{array}{ll}1 & 4 \\ 1 & 3\end{array}\right) \text{ is invertible because its determinant is not equal to zero, i.e., } \operatorname{det}(A) \neq 0\}.\)
