Mathematics II20765 marksNumerical: matrix commutativityMatrix operations
Let A and B be matrices. Determine the value(s) of k if any will make AB = BA.
Let A and B be matrices. Determine the value(s) of k if any will make AB = BA.
$$A = \begin{bmatrix} 2 & 5 \ -3 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & -5 \ 3 & k \end{bmatrix}$$
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$$A = \begin{bmatrix} 2 & 5 \ -3 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & -5 \ 3 & k \end{bmatrix}$$ Requirement: find $k$ (if any) such that $AB = BA$. $$AB = \begin{bmatrix} 2 & 5 \ -3 & 1 \end{bmatrix}\begin{bmatrix} 4 & -5 \ 3 & k \end{bmatrix}$$ $$AB = \begin{bmatrix} (2)(4)+(5)(...