Question
There is No Inverse for the following matrix
Matrix A =6 -3
-2 1
Matrix A =6 -3
-2 1
Answers
GPT-4o mini
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.
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.
d
is it true or false
GPT-4o mini
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.