Find the values of a and b if A = B, where \(A=\begin{bmatrix} a+4& 3

1.	Find the values of a and b if A = B, where \(A=\begin{bmatrix} a+4& 3b \\[0.3em] 8 & -6 \\[0.3em] \end{bmatrix},\)\(B=\begin{bmatrix} 2a+2&b^2+2 \\[0.3em] 8 & b^2-10 \\[0.3em] \end{bmatrix} \)
Answer» Given two matrices are equal. i.e, A = B. \(\begin{bmatrix} a+4& 3b \\[0.3em] 8 & -6 \\[0.3em] \end{bmatrix}\)\(=\begin{bmatrix} 2a+2&b^2+2 \\[0.3em] 8 & b^2-10 \\[0.3em] \end{bmatrix} \) We know that if two matrices are equal then the elements of each matrices are also equal. ∴ a + 4 = 2a + 2 ⇒ a – 2a = 2 – 4 ⇒ – a = – 2 ⇒ a = 2 … (1) And 3b = b² + 2 ⇒ b² – 3b + 2 = 0 ⇒ b² – 2b – b + 2 = 0 ⇒ b(b – 2) – 1(b – 2) = 0 ⇒ (b – 2)(b – 1) = 0 ⇒ b = 2 or 1 … (2) And – 6 = b² – 10 ⇒ b² = – 10 + 6 ⇒ b² = – 4 ⇒ b = ±2i (No real solution) … (3) ∴ a = 2, b = 2 or 1

Find the values of a and b if A = B, where \(A=\begin{bmatrix} a+4& 3b \\[0.3em] 8 & -6 \\[0.3em] \end{bmatrix},\)\(B=\begin{bmatrix} 2a+2&b^2+2 \\[0.3em] 8 & b^2-10 \\[0.3em] \end{bmatrix} \)

Answer»

Given two matrices are equal.

i.e, A = B.

\(\begin{bmatrix} a+4& 3b \\[0.3em] 8 & -6 \\[0.3em] \end{bmatrix}\)\(=\begin{bmatrix} 2a+2&b^2+2 \\[0.3em] 8 & b^2-10 \\[0.3em] \end{bmatrix} \)

We know that if two matrices are equal then the elements of each matrices are also equal.

∴ a + 4 = 2a + 2

⇒ a – 2a = 2 – 4

⇒ – a = – 2

⇒ a = 2 … (1)

And 3b = b² + 2

⇒ b² – 3b + 2 = 0

⇒ b² – 2b – b + 2 = 0

⇒ b(b – 2) – 1(b – 2) = 0

⇒ (b – 2)(b – 1) = 0

⇒ b = 2 or 1 … (2)

And – 6 = b² – 10

⇒ b² = – 10 + 6

⇒ b² = – 4

⇒ b = ±2i

(No real solution) … (3)

∴ a = 2, b = 2 or 1

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Find the values of a and b if A = B, where \(A=\begin{bmatrix} a+4&amp; 3b \\[0.3em] 8 &amp; -6 \\[0.3em] \end{bmatrix},\)\(B=\begin{bmatrix} 2a+2&amp;b^2+2 \\[0.3em] 8 &amp; b^2-10 \\[0.3em] \end{bmatrix} ​​\)

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Find the values of a and b if A = B, where \(A=\begin{bmatrix} a+4& 3b \\[0.3em] 8 & -6 \\[0.3em] \end{bmatrix},\)\(B=\begin{bmatrix} 2a+2&b^2+2 \\[0.3em] 8 & b^2-10 \\[0.3em] \end{bmatrix} \)