Math  /  Algebra

QuestionFind the following matrices where A=[863083]A=\left[\begin{array}{rr}8 & 6 \\ 3 & 0 \\ -8 & 3\end{array}\right] and B=[830653]B=\left[\begin{array}{rr}-8 & 3 \\ 0 & 6 \\ -5 & -3\end{array}\right]. a. A+BA+B b. -4 A c. 8A+3B-8 A+3 B a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A+B=A+B= \square (Simplify your answers.) B. This matrix operation is not possible. b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice α0\alpha_{0} A. 4 A=-4 \mathrm{~A}= \square (Simplify your answers.) B. This matrix operation is not possible. c. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
\square A. 8A+3B=-8 A+3 B=\square (Simplify your answers.) B. This matrix operation is not possible.

Studdy Solution
Calculate 8A+3B-8A + 3B.
First, calculate 8A-8A:
\[ -8A = -8 \times \left[\begin{array}{rr}8 & 6 \\ 3 & 0 \\ -8 & 3\end{array}\right] $
\[ -8A = \left[\begin{array}{rr}-64 & -48 \\ -24 & 0 \\ 64 & -24\end{array}\right] $
Next, calculate 3B3B:
\[ 3B = 3 \times \left[\begin{array}{rr}-8 & 3 \\ 0 & 6 \\ -5 & -3\end{array}\right] $
\[ 3B = \left[\begin{array}{rr}-24 & 9 \\ 0 & 18 \\ -15 & -9\end{array}\right] $
Now, add 8A-8A and 3B3B:
\[ -8A + 3B = \left[\begin{array}{rr}-64 & -48 \\ -24 & 0 \\ 64 & -24\end{array}\right] + \left[\begin{array}{rr}-24 & 9 \\ 0 & 18 \\ -15 & -9\end{array}\right] $
Add corresponding elements:
\[ -8A + 3B = \left[\begin{array}{rr}-64 + (-24) & -48 + 9 \\ -24 + 0 & 0 + 18 \\ 64 + (-15) & -24 + (-9)\end{array}\right] $
\[ -8A + 3B = \left[\begin{array}{rr}-88 & -39 \\ -24 & 18 \\ 49 & -33\end{array}\right] $
The solutions are: a. A+B=[0936130] A + B = \left[\begin{array}{rr}0 & 9 \\ 3 & 6 \\ -13 & 0\end{array}\right] b. 4A=[32241203212]-4A = \left[\begin{array}{rr}-32 & -24 \\ -12 & 0 \\ 32 & -12\end{array}\right] c. 8A+3B=[883924184933]-8A + 3B = \left[\begin{array}{rr}-88 & -39 \\ -24 & 18 \\ 49 & -33\end{array}\right]

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