Question

-2

If A = [ 24 1² 3], B = [15], C = [2²] and D =
11
-6 12
8
-1 17] find:

Answer 1

`\textsf{8.} \quad C-B =\left[\begin{array}{r} -24\\30\end{array}\right]`

`\textsf{9.} \quad B+D= \sf und\:\!efined`

`\textsf{11.} \quad 2A-D = \left[\begin{array}{rrr}20&-16&-2 \\-8&23&-17\end{array}\right]`

Explanation:

Given matrices:

`A=\left[\begin{array}{rrl}7 & -2 & 3 \\-4 & 11 & 0\end{array}\right]`

`B=\left[\begin{array}{r} 15\\-6\end{array}\right]`

`C=\left[\begin{array}{r} -9\\24\end{array}\right]`

`D=\left[\begin{array}{rrr}-6 & 12 & 8\\0 & -1 & 17\end{array}\right]`

Question 8

`\begin{aligned}C-B & =\left[\begin{array}{r} -9\\24\end{array}\right]-\left[\begin{array}{r} 15\\-6\end{array}\right]\\\\ & =\left[\begin{array}{r} (-9-15)\\(24-(-6))\end{array}\right]\\\\ & =\left[\begin{array}{r} -24\\30\end{array}\right]\end{aligned}`

Question 9

Matrix B has a dimension of 2×1 whilst matrix D has a dimension of 2×3.

As the number of rows and columns don’t match, the sum of matrices B and D doesn’t exist or is undefined.

Question 11

`\begin{aligned}2A-D & = 2\left[\begin{array}{rrr}7 & -2 & 3 \\-4 & 11 & 0\end{array}\right]-\left[\begin{array}{rrr}-6 & 12 & 8\\0 & -1 & 17\end{array}\right]\\\\& = \left[\begin{array}{rrr}14 & -4 & 6 \\-8 & 22 & 0\end{array}\right]-\left[\begin{array}{rrr}-6 & 12 & 8\\0 & -1 & 17\end{array}\right]\\\\& = \left[\begin{array}{rrr}(14-(-6)) & (-4-12) & (6-8) \\(-8-0) & (22-(-1)) & (0-17)\end{array}\right]\\\\& = \left[\begin{array}{rrr}20&-16&-2 \\-8&23&-17\end{array}\right]\end{aligned}`