Answers: Matrix multiplication
These are the answers to Questions: Matrix multiplication.
Please attempt the questions before reading these answers!
Q1
\(\displaystyle \quad Q R = \begin{bmatrix} 27+\pi \end{bmatrix}\)
\(\displaystyle \quad R Q = \begin{bmatrix} -2 & -3 & -1 & -4 \\6 & 9 & 3 & 12 \\2\pi & 3\pi & \pi & 4\pi \\10& 15 & 5 &20 \end{bmatrix}\)
This is undefined as \(Q\) has \(4\) columns and \(S\) has \(2\) rows.
\(\displaystyle \quad ST = \begin{bmatrix} -9 & 30 \\ 13 & 18 \end{bmatrix}\)
\(S^2\) is undefined as \(S\) has \(3\) columns and \(S\) has \(2\) rows.
\(\displaystyle \quad TS = \begin{bmatrix} 23 & -34 & 31 \\ 1 & -6 & 33 \\ -24 & 32 & -8 \end{bmatrix}\)
\(\quad UV = \begin{bmatrix} 6-\sqrt{2} & 29/2 \\-12+3\sqrt{2} & -59/2 \end{bmatrix}\)
\(\quad VU = \begin{bmatrix} -3/2-\sqrt{2} & 2+2\sqrt{2} \\18 & -22 \end{bmatrix}\)
\(\quad WR = \begin{bmatrix} -3 + 7\pi \\ -45 + 5\pi \\44 +3\sqrt{7} - 8\pi \end{bmatrix}\)
\(\quad SW = \begin{bmatrix} -1 & 7 + 5\sqrt{7} & -48 & 57 + \pi\\ 11 & -13 -\sqrt{7} & 22 & -33-3\pi \end{bmatrix}\)
\(SX\) is undefined as \(S\) has \(3\) columns and \(X\) has \(2\) rows.
\(\quad T U = \begin{bmatrix} -23 & 34 \\-1 & 6 \\ 24 & -32 \end{bmatrix}\)
\(\quad T V = \begin{bmatrix} 18-5\sqrt{2} & -89/2 \\6+7\sqrt{2} & 21/2 \\24 & 56 \end{bmatrix}\)
\(\quad T X = \begin{bmatrix} 17 \\29 \\4 \end{bmatrix}\)
\(\quad U X = \begin{bmatrix} -3 \\10 \end{bmatrix}\)
\(\quad V X = \begin{bmatrix} -1/4 + 4\sqrt{2} \\31/2 \end{bmatrix}\)
\(\quad X Q = \begin{bmatrix} -8 & 12 & 4 & 16 \\ 1 & 3/2 & 1/2 & 2 \end{bmatrix}\)
\(\quad V V = \begin{bmatrix} 1/2 & -7/2 -\sqrt{2} /2 \\21+3\sqrt{2} & 95/2 \end{bmatrix}\)
\(\quad U U = \begin{bmatrix} 7 & -10 \\-15 & 22 \end{bmatrix}\)
\(\quad U X Q = \begin{bmatrix} -6 & -9 & -3 & -12 \\20 & 30 & 10 & 40 \end{bmatrix}\)
\(\quad U^3 = \begin{bmatrix} -37 & 54 \\ 81 & -118 \end{bmatrix}\)
\(W^2\) is undefined, as \(W\) has \(4\) columns but only \(3\) rows.
\(\quad S T U = \begin{bmatrix} 99 & -138 \\ 41 & -46 \end{bmatrix}\)
\(\quad T X Q R = \begin{bmatrix} 459 +17\pi \\783 + 29\pi \\108 +4\pi \end{bmatrix}\)
\(\quad 3U X = \begin{bmatrix} -18 \\60 \end{bmatrix}\)
\(\quad (S T)-2U = \begin{bmatrix} -11 & 26 \\7 & 10 \end{bmatrix}\)
\(\quad W R + T X = \begin{bmatrix} 14+7\pi \\-16 +5\pi \\18+ 3\sqrt{7} -8\pi \end{bmatrix}\)
\(\quad -R Q R = \begin{bmatrix} 27+\pi \\-81 -3\pi \\-27\pi + \pi^2 \\135+ 5\pi \end{bmatrix}\)
\(\quad (V+U) X = \begin{bmatrix} -5-3\sqrt{2} \\61 \end{bmatrix}\)
\(\quad 4U^2 + V^2 = \begin{bmatrix} 57/2 & -87/2 - \sqrt{2}/2 \\-39+3\sqrt{2} & 271/2 \end{bmatrix}\)
Version history
v1.0: initial version created 04/25 by Jessica Taberner as part of a University of St Andrews VIP project.