Question

3. (a) For the following matrices, calculate AB, BA, $AB^T$ and $B^TA$ if possible. If not, explain why. $\begin{pmatrix} 0 & -1 & 0 \ 4 & 9 & 2 \ 8 & -1 & 7 \end{pmatrix}$, $B = \begin{pmatrix} 2 & 1 \ -3 & 4 \ 1 & 6 \end{pmatrix}$ (b) Solve the given equation for X. $A = \begin{pmatrix} -4 & 0 \ 1 & -5 \ -3 & 2 \end{pmatrix}$, $B = \begin{pmatrix} 1 & 2 \ -2 & 1 \ 4 & 4 \end{pmatrix}$, $3X + 2A = B$ 4. Prove that if A and B are symmetrical matrices and AB = BA then AB is also a symmetrical matrix.

          3.
(a) For the following matrices, calculate AB, BA, $AB^T$ and $B^TA$ if possible. If not, explain why.
$\begin{pmatrix} 0 & -1 & 0 \ 4 & 9 & 2 \ 8 & -1 & 7 \end{pmatrix}$, $B = \begin{pmatrix} 2 & 1 \ -3 & 4 \ 1 & 6 \end{pmatrix}$
(b) Solve the given equation for X.
$A = \begin{pmatrix} -4 & 0 \ 1 & -5 \ -3 & 2 \end{pmatrix}$, $B = \begin{pmatrix} 1 & 2 \ -2 & 1 \ 4 & 4 \end{pmatrix}$, $3X + 2A = B$
4. Prove that if A and B are symmetrical matrices and AB = BA then AB is also a symmetrical matrix.

3.
(a) For the following matrices, calculate AB, BA, AB^T and B^TA if possible. If not, explain why.
< p m a t r i x >, B =
< p m a t r i x >
(b) Solve the given equation for X.
A =
< p m a t r i x >, B =
< p m a t r i x >, 3X + 2A = B
4. Prove that if A and B are symmetrical matrices and AB = BA then AB is also a symmetrical matrix.

Added by John B.

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