Question

There is No Inverse for the following matrix
Matrix A =6 -3
-2 1

Answer 1

is it true or false

Answer 2

To determine if a matrix has an inverse, we can check its determinant. If the determinant is zero, the matrix does not have an inverse; if it is non-zero, the matrix has an inverse.

For your matrix \( A \):

\[
A = \begin{pmatrix}
6 & -3 \\
-2 & 1
\end{pmatrix}
\]

The formula for the determinant of a \( 2 \times 2 \) matrix:

\[
\text{det}(A) = ad - bc
\]

where \( a, b, c, d \) are the elements of the matrix:

\[
\text{det}(A) = (6)(1) - (-3)(-2) = 6 - 6 = 0
\]

Since the determinant of matrix \( A \) is \( 0 \), it is confirmed that matrix \( A \) does not have an inverse.

Answer 3

True. The statement "There is no inverse for the matrix \( A = \begin{pmatrix} 6 & -3 \\ -2 & 1 \end{pmatrix} \)" is true because the determinant of the matrix is zero, which means that the matrix does not have an inverse.