If A = [3241]\begin{bmatrix} 3 & 2 \ 4 & 1 \end{bmatrix}[3421] and B = [5032]\begin{bmatrix} 5 & 0 \ 3 & 2 \end{bmatrix}[5302], then (3A + 2B) is equal to:
[196187]\begin{bmatrix} 19 & 6 \ 18 & 7 \end{bmatrix}[191867]
[8273]\begin{bmatrix} 8 & 2 \ 7 & 3 \end{bmatrix}[8723]
[19161817]\begin{bmatrix} 19 & 16 \ 18 & 17 \end{bmatrix}[19181617]
[916817]\begin{bmatrix} 9 & 16 \ 8 & 17 \end{bmatrix}[981617]
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Given,
A = [3241]\begin{bmatrix} 3 & 2 \ 4 & 1 \end{bmatrix}[3421] and B = [5032]\begin{bmatrix} 5 & 0 \ 3 & 2 \end{bmatrix}[5302]
Solving for 3A + 2B:
⇒3[3241]+2[5032]⇒[96123]+[10064]⇒3[3241]+2[5032]⇒[9+106+012+63+4]⇒[196187]\Rightarrow 3\begin{bmatrix} 3 & 2 \ 4 & 1 \end{bmatrix} + 2\begin{bmatrix} 5 & 0 \ 3 & 2 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 9 & 6 \ 12 & 3 \end{bmatrix} + \begin{bmatrix} 10 & 0 \ 6 & 4 \end{bmatrix} \\[1em] \Rightarrow 3\begin{bmatrix} 3 & 2 \ 4 & 1 \end{bmatrix} + 2\begin{bmatrix} 5 & 0 \ 3 & 2 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 9 + 10 & 6 + 0 \ 12 + 6 & 3 + 4 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 19 & 6 \ 18 & 7 \end{bmatrix}⇒3[3421]+2[5302]⇒[91263]+[10604]⇒3[3421]+2[5302]⇒[9+1012+66+03+4]⇒[191867]
Hence, option 1 is the correct option.
Answered By
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[77−412]\begin{bmatrix} 7 & 7 \ -4 & 12 \end{bmatrix}[7−4712]
[−774−12]\begin{bmatrix} -7 & 7 \ 4 & -12 \end{bmatrix}[−747−12]
[−7−7412]\begin{bmatrix} -7 & -7 \ 4 & 12 \end{bmatrix}[−74−712]
[312−4]\begin{bmatrix} 3 & 1 \ 2 & -4 \end{bmatrix}[321−4]
If A = [42−3−9]\begin{bmatrix} 4 & 2 \ -3 & -9 \end{bmatrix}[4−32−9], then the value of (-3)A is:
[−8−4618]\begin{bmatrix} -8 & -4 \ 6 & 18 \end{bmatrix}[−86−418]
[−12−6918]\begin{bmatrix} -12 & -6 \ 9 & 18 \end{bmatrix}[−129−618]
[−12−6927]\begin{bmatrix} -12 & -6 \ 9 & 27 \end{bmatrix}[−129−627]
[−1269−27]\begin{bmatrix} -12 & 6 \ 9 & -27 \end{bmatrix}[−1296−27]
Find the matrix A, if A + [46−37]\begin{bmatrix} 4 & 6 \ -3 & 7 \end{bmatrix}[4−367] = [3−65−8]\begin{bmatrix} 3 & -6 \ 5 & -8 \end{bmatrix}[35−6−8]
[−1128−15]\begin{bmatrix} -1 & 12 \ 8 & -15 \end{bmatrix}[−1812−15]
[−1−128−15]\begin{bmatrix} -1 & -12 \ 8 & -15 \end{bmatrix}[−18−12−15]
[−1−12−8−15]\begin{bmatrix} -1 & -12 \ -8 & -15 \end{bmatrix}[−1−8−12−15]
[112815]\begin{bmatrix} 1 & 12 \ 8 & 15 \end{bmatrix}[181215]
cosθ⋅[cosθsinθ−sinθcosθ]+sinθ⋅[sinθ−cosθcosθsinθ]\cosθ \cdot \begin{bmatrix} \cosθ & \sinθ \ -\sinθ & \cosθ \end{bmatrix} + \sinθ \cdot \begin{bmatrix} \sinθ & -\cosθ \ \cosθ & \sinθ \end{bmatrix}cosθ⋅[cosθ−sinθsinθcosθ]+sinθ⋅[sinθcosθ−cosθsinθ] is equal to:
[1111]\begin{bmatrix} 1 & 1 \ 1 & 1 \end{bmatrix}[1111]
[0110]\begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix}[0110]
[1001]\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}[1001]
none of these
