If A =[12−23], B =[−2−112] and C=[032−1]\text{If A } = \begin{bmatrix}[r] 1 & 2 \ -2 & 3 \end{bmatrix}, \text{ B } = \begin{bmatrix}[r] -2 & -1 \ 1 & 2 \end{bmatrix} \text{ and C} = \begin{bmatrix}[r] 0 & 3 \ 2 & -1 \end{bmatrix}If A =[1−223], B =[−21−12] and C=[023−1], find A + 2B - 3C.
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A + 2B - 3C =[12-23]+2[-2−112]−3[032−1]=[12-23]+[-4−224]−[096−3]=[1+(−4)−02+(−2)−9-2+2−63+4−(−3)]=[-3−9-610]\text{A + 2B - 3C }= \begin{bmatrix}[r] 1 & 2 \ -2 & 3 \end{bmatrix} + 2\begin{bmatrix}[r] -2 & -1 \ 1 & 2 \end{bmatrix} - 3\begin{bmatrix}[r] 0 & 3 \ 2 & -1 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 1 & 2 \ -2 & 3 \end{bmatrix} + \begin{bmatrix}[r] -4 & -2 \ 2 & 4 \end{bmatrix} - \begin{bmatrix}[r] 0 & 9 \ 6 & -3 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 1 + (-4) - 0 & 2 + (-2) - 9 \ -2 + 2 - 6 & 3 + 4 - (-3) \end{bmatrix} \\[1em] = \begin{bmatrix}[r] -3 & -9 \ -6 & 10 \end{bmatrix}A + 2B - 3C =[1-223]+2[-21−12]−3[023−1]=[1-223]+[-42−24]−[069−3]=[1+(−4)−0-2+2−62+(−2)−93+4−(−3)]=[-3-6−910]
Hence, the matrix A + 2B - 3C = [−3−9−610].\begin{bmatrix}[r] -3 & -9 \ -6 & 10 \end{bmatrix}.[−3−6−910].
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If A =[20−31] and B =[01−23]\text{If A }= \begin{bmatrix}[r] 2 & 0 \ -3 & 1 \end{bmatrix} \text{ and B }= \begin{bmatrix}[r] 0 & 1 \ -2 & 3 \end{bmatrix}If A =[2−301] and B =[0−213], find 2A - 3B.
Simplify : sin A[sin A−cos Acos Asin A]+cos A[cos Asin A−sin Acos A]\text{sin A}\begin{bmatrix}[r] \text{sin A} & -\text{cos A} \ \text{cos A} & \text{sin A} \end{bmatrix} + \text{cos A}\begin{bmatrix}[r] \text{cos A} & \text{sin A} \ -\text{sin A} & \text{cos A} \end{bmatrix}sin A[sin Acos A−cos Asin A]+cos A[cos A−sin Asin Acos A].
If A = [0−112] and B=[12−11]\begin{bmatrix}[r] 0 & -1 \ 1 & 2 \end{bmatrix} \text{ and B} = \begin{bmatrix}[r] 1 & 2 \ -1 & 1 \end{bmatrix}[01−12] and B=[1−121], find the matrix X if
(i) 3A + X = B
(ii) X - 3B = 2A.
Solve the matrix equation [2150]−3X=[−7426]\begin{bmatrix} 2 & 1 \ 5 & 0 \end{bmatrix} - 3X = \begin{bmatrix}[r] -7 & 4 \ 2 & 6 \end{bmatrix}[2510]−3X=[−7246]
