Questions: Matrix multiplication
Before attempting these questions, it is highly recommended that you read Guide: Matrix multiplication.
You are given the following matrices:
\(Q = \begin{bmatrix} 2 & 3 & 1 & 4 \end{bmatrix},\) \(\;\;R = \begin{bmatrix} -1 \\ 3 \\ \pi \\ 5 \end{bmatrix},\) \(\;\;S = \begin{bmatrix} 1 & -2 & 5 \\ -3 & 4 & -1 \end{bmatrix},\) \(\;\;T = \begin{bmatrix} 5 & -6 \\ 7 & 2 \\ 0 & 8 \end{bmatrix},\)
\(U = \begin{bmatrix} -1 & 2 \\ 3 & -4 \end{bmatrix},\) \(\;\;V = \begin{bmatrix} \sqrt{2} & -1/2 \\ 3 & 7 \end{bmatrix},\) \(\;\;W = \begin{bmatrix} 0 & -1 & 2 & \pi \\ 3 & -4 & 5 & -6 \\ 1 & \sqrt{7} & -8 & 9 \end{bmatrix},\) \(\;\;X = \begin{bmatrix} 4 \\ 1/2 \end{bmatrix}.\)
Calculate the following using matrix multiplications. If they are undefined, state that they are undefined and give a reason why. You should give exact answers, and not use decimals.
\(\quad QR\)
\(\quad RQ\)
\(\quad QS\)
\(\quad ST\)
\(\quad S^2\)
\(\quad TS\)
\(\quad UV\)
\(\quad VU\)
\(\quad WR\)
\(\quad SW\)
\(\quad SX\)
\(\quad TU\)
\(\quad TV\)
\(\quad TX\)
\(\quad UX\)
\(\quad VX\)
\(\quad XQ\)
\(\quad V^2\)
\(\quad U^2\)
\(\quad UXQ\)
\(\quad U^3\)
\(\quad W^2\)
\(\quad S T V\)
\(\quad T X Q R\)
\(\quad 3U X\)
\(\quad (S T)-2U\)
\(\quad W R + T X\)
\(\quad -R Q R\)
\(\quad (V+U)X\)
\(\quad 4U^2 + V^2\)
After attempting the questions above, please click this link to find the answers.
Version history
v1.0: initial version created 04/25 by Jessica Taberner as part of a University of St Andrews VIP project.