If A = [3724], B =[0253] and C =[1−5−46],\begin{bmatrix}[r] 3 & 7 \ 2 & 4 \end{bmatrix}, \text{ B } = \begin{bmatrix}[r] 0 & 2 \ 5 & 3 \end{bmatrix} \text{ and C } = \begin{bmatrix}[r] 1 & -5 \ -4 & 6 \end{bmatrix},[3274], B =[0523] and C =[1−4−56], find AB - 5C.
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AB−5C=[3724][0253]−5[1−5−46]=[3×0+7×53×2+7×32×0+4×52×2+4×3]-[5−25−2030]=[0+356+210+204+12]-[5−25−2030]=[35−527−(−25)20−(−20)16−30]=[305240−14]AB - 5C = \begin{bmatrix}[r] 3 & 7 \ 2 & 4 \end{bmatrix}\begin{bmatrix}[r] 0 & 2 \ 5 & 3 \end{bmatrix} - 5\begin{bmatrix}[r] 1 & -5 \ -4 & 6 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 3 \times 0 + 7 \times 5 & 3 \times 2 + 7 \times 3 \ 2 \times 0 + 4 \times 5 & 2 \times 2 + 4 \times 3 \end{bmatrix} \\[1em] - \begin{bmatrix}[r] 5 & -25 \ -20 & 30 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 0 + 35 & 6 + 21 \ 0 + 20 & 4 + 12 \end{bmatrix} - \begin{bmatrix}[r] 5 & -25 \ -20 & 30 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 35 - 5 & 27 - (-25) \ 20 - (-20) & 16 - 30 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 30 & 52 \ 40 & -14 \end{bmatrix}AB−5C=[3274][0523]−5[1−4−56]=[3×0+7×52×0+4×53×2+7×32×2+4×3]-[5−20−2530]=[0+350+206+214+12]-[5−20−2530]=[35−520−(−20)27−(−25)16−30]=[304052−14]
Hence, the matrix AB - 5C = [305240−14].\begin{bmatrix}[r] 30 & 52 \ 40 & -14 \end{bmatrix}.[304052−14].
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If A = [354−2] and B =[24],\begin{bmatrix}[r] 3 & 5 \ 4 & -2 \end{bmatrix} \text{ and B } = \begin{bmatrix}[r] 2 \ 4 \end{bmatrix},[345−2] and B =[24], is the product AB possible? Give a reason. If yes find AB.
If A = [2513], B =[1−1−32],\begin{bmatrix}[r] 2 & 5 \ 1 & 3 \end{bmatrix}, \text{ B } = \begin{bmatrix}[r] 1 & -1 \ -3 & 2 \end{bmatrix},[2153], B =[1−3−12], find AB and BA. Is AB = BA ?
If A = [1221] and B =[2112],\begin{bmatrix}[r] 1 & 2 \ 2 & 1 \end{bmatrix} \text{ and B } = \begin{bmatrix}[r] 2 & 1 \ 1 & 2 \end{bmatrix},[1221] and B =[2112], find A(BA).
Given the matrices :
A =[2142], B =[34−1−2] and C =[−310−2].\text { A } = \begin{bmatrix}[r] 2 & 1 \ 4 & 2 \end{bmatrix}, \text{ B } = \begin{bmatrix}[r] 3 & 4 \ -1 & -2 \end{bmatrix} \text{ and C } = \begin{bmatrix}[r] -3 & 1 \ 0 & -2 \end{bmatrix} . A =[2412], B =[3−14−2] and C =[−301−2].
Find the products of (i) ABC (ii) ACB and state whether they are equal.
