Mathematics II20805 marksNumerical: matrix commutativity valueMatrix operations
Let A = beginbmatrix 1 & 5 -3 & 1 endbmatrix, B = beginbmatrix 4 & -5 3 & k endbmatrix What value(s) of k, if any, will make AB = BA?
Let $A = \begin{bmatrix} 1 & 5 \ -3 & 1 \end{bmatrix}$, $B = \begin{bmatrix} 4 & -5 \ 3 & k \end{bmatrix}$
What value(s) of k, if any, will make AB = BA? [5]
$$A = \begin{bmatrix} 1 & 5 \ -3 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & -5 \ 3 & k \end{bmatrix}$$ We must find $k$ (if any) so that $AB = BA$. --- $$AB = \begin{bmatrix} 1 & 5 \ -3 & 1 \end{bmatrix} \begin{bmatrix} 4 & -5 \ 3 & k \end{bmatrix}$$ Entry by entry: -