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  • Find the value of a, b, c and d, if 3[a bc d] = [a 6 -1 2d]

Find the value of a, b, c and d, if 3\left[\begin{array}{ll} \mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{d} \end{array}\right]=\left[\begin{array}{cc} \mathrm{a} & 6 \\ -1 & 2 \mathrm{~d} \end{array}\right]+\left[\begin{array}{cc} 4 & \mathrm{a}+\mathrm{b} \\ \mathrm{c}+\mathrm{d} & 3 \end{array}\right]

Answers (1)

We are given the following matrices,

3\left[\begin{array}{ll} \mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{d} \end{array}\right]=\left[\begin{array}{cc} \mathrm{a} & 6 \\ -1 & 2 \mathrm{~d} \end{array}\right]+\left[\begin{array}{cc} 4 & \mathrm{a}+\mathrm{b} \\ \mathrm{c}+\mathrm{d} & 3 \end{array}\right]

We need to determine the value of a, b, c and d.

\begin{array}{l} \text { As, } 3\left[\begin{array}{ll} \text { a } & b \\ c & d \end{array}\right]=\left[\begin{array}{cc} a & 6 \\ -1 & 2 d \end{array}\right]+\left[\begin{array}{cc} 4 & a+b \\ c+d & 3 \end{array}\right] \\ \Rightarrow\left[\begin{array}{ll} 3 a & 3 b \\ 3 c & 3 d \end{array}\right]=\left[\begin{array}{cc} a+4 & 6+a+b \\ -1+c+d & 2 d+3 \end{array}\right] \end{array}

As both matrices are equal so their corresponding elements must also be equal.

\\$ \therefore $ 3a = a + 4 \\$ \Rightarrow $ 2a = 4 \\$ \Rightarrow $ a = 2

Similarly,

$ \Rightarrow $ 2b = 6 + a

As from above a = 2

\\3b = 6 + a + b \\$ \therefore $ 2b = 6+2 = 8 \\$ \Rightarrow $ b = 4 \\Also 3d = 2d + 3 \\$ \Rightarrow $ d = 3

And, we have,

\\3c = -1 + c + d \\$ \Rightarrow $ 2c = d - 1 \\$ \Rightarrow $ 2c = 3-1 \\$ \Rightarrow $ c = 2/2 = 1 \\Thus, a = 2, b = 4, c = 1 $ and d = 3.

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