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ICSE Class X Math 2016 Paper

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Given A=[4sin⁡30∘cos⁡0∘cos⁡0∘4sin⁡30∘]A = \begin{bmatrix} 4 \sin 30^{\circ} & \cos 0^{\circ} \\ \cos 0^{\circ} & 4 \sin 30^{\circ} \end{bmatrix} and B=[45]B = \begin{bmatrix} 4 \\ 5 \end{bmatrix} If AX=BA X = B
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Question : 27 of 57
Marks: +1, -0
Write the order of matrix XX.
Solution:  
 Given : A=[4sin⁡30∘cos⁡0∘cos⁡0∘4sin⁡30∘]\text{ Given : } A = \begin{bmatrix} 4 \sin 30^{\circ} & \cos 0^{\circ} \\ \cos 0^{\circ} & 4 \sin 30^{\circ} \end{bmatrix}  and B=[45]\text{ and } B = \begin{bmatrix} 4 \\ 5 \end{bmatrix}
Order of A=2×2A = 2 \times 2 , Order of B=2×1B = 2 \times 1
Also given: AX=BAX = B
[]2×2[]2×1=[]2×1\left[ \right]_{2 \times 2} \left[ \right]_{2 \times 1} = \left[ \right]_{2 \times 1}
∴\therefore Order of X=2×1X = 2 \times 1
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