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.
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2A - 3B =2[20−31]−3[01−23]=[40−62]−[03−69]=[4+00−3−6−(−6)2−9]=[4−30−7]\text{2A - 3B }= 2\begin{bmatrix}[r] 2 & 0 \ -3 & 1 \end{bmatrix} - 3\begin{bmatrix}[r] 0 & 1 \ -2 & 3 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 4 & 0 \ -6 & 2 \end{bmatrix} - \begin{bmatrix}[r] 0 & 3 \ -6 & 9 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 4 + 0 & 0 - 3 \ -6 - (-6) & 2 - 9 \end{bmatrix} \\[1em] = \begin{bmatrix}[r] 4 & -3 \ 0 & -7 \end{bmatrix} \\[1em]2A - 3B =2[2−301]−3[0−213]=[4−602]−[0−639]=[4+0−6−(−6)0−32−9]=[40−3−7]
Hence, the matrix 2A - 3B = [4−30−7].\begin{bmatrix}[r] 4 & -3 \ 0 & -7 \end{bmatrix}.[40−3−7].
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Find the values of a, b, c and d if [a+b35+cab]=[6d−18].\begin{bmatrix}[r] a + b & 3 \ 5 + c & ab \end{bmatrix} = \begin{bmatrix}[r] 6 & d \ -1 & 8 \end{bmatrix} .[a+b5+c3ab]=[6−1d8].
Given that M=[2012] and N =[20−12]\text{M} = \begin{bmatrix}[r] 2 & 0 \ 1 & 2 \end{bmatrix} \text{ and N }= \begin{bmatrix}[r] 2 & 0 \ -1 & 2 \end{bmatrix}M=[2102] and N =[2−102], find M + 2N.
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 =[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.
