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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES3 Marks
Question
Find the values of a, b, c and d if:$3\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}=\begin{bmatrix}\text{a}&6\\-1&2\text{d}\end{bmatrix}+\begin{bmatrix}4&\text{a}+\text{b}\\\text{c}+\text{d}&3\end{bmatrix}.$
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Answer

Consider, $3\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}=\begin{bmatrix}\text{a}&6\\-1&2\text{d}\end{bmatrix}+\begin{bmatrix}4&\text{a}+\text{b}\\\text{c}+\text{d}&3\end{bmatrix}$$\Rightarrow\ \begin{bmatrix}3\text{a}&3\text{b}\\3\text{c}&3\text{d}\end{bmatrix}=\begin{bmatrix}\text{a}+4&6+\text{a}+\text{b}\\\text{c}+\text{d}-1&3+2\text{d}\end{bmatrix}$
By equality of matrices, we get
3a = a + 4, 3b = 6 + a + b and 3d = 3 + 2d
⇒ a = 2, b = 4 and d = 3.

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