If the trace of two matrices A- 2a2 5- 3 9-6b- - and B- -b2 5- 3 8a-8- - are equal-where a-b- then 2a-b equals to

From given matrices, Tr(A)=2a^2+9 6b Tr(B)= b^2+8a 8 As, Tr(A)=Tr(B) ⇒ 2a^2+9 6b= b^2+8a 8 ⇒ 2(a^2 4a+4)+b^2 6b+9=0 ⇒ 2(a 2)^2+(b 3)^2=0 ⇒ a 2=0 and b 3=0 ⇒ a=2 ...

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Byju's Answer

Standard XII

Mathematics

Transpose of a Matrix

If the trace ...

Question

If the trace of two matrices $A = [\begin{matrix} 2 a^{2} & 5 3 & 9 - 6 b \end{matrix}]$ and $B = [\begin{matrix} - b^{2} & 5 3 & 8 a - 8 \end{matrix}]$ are equal,where $a, b \in R,$ then $2 a - b$ equals to

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Solution

The correct option is B $1$
From given matrices, $T r (A) = 2 a^{2} + 9 - 6 b$
$T r (B) = - b^{2} + 8 a - 8$
As, $T r (A) = T r (B)$
$\Rightarrow 2 a^{2} + 9 - 6 b = - b^{2} + 8 a - 8 \Rightarrow 2 (a^{2} - 4 a + 4) + b^{2} - 6 b + 9 = 0 \Rightarrow 2 (a - 2)^{2} + (b - 3)^{2} = 0$
$\Rightarrow a - 2 = 0$ and $b - 3 = 0$
$\Rightarrow a = 2, b = 3$
So, $2 a - b = 1$

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If the trace of two matrices A=[2a2539−6b] and B=[−b2538a−8] are equal,where a,b∈R, then 2a−b equals to

The correct option is B 1From given matrices, Tr(A)=2a2+9−6b Tr(B)=−b2+8a−8 As, Tr(A)=Tr(B) ⇒2a2+9−6b=−b2+8a−8⇒2(a2−4a+4)+b2−6b+9=0⇒2(a−2)2+(b−3)2=0 ⇒a−2=0 and b−3=0 ⇒a=2,b=3 So, 2a−b=1

If the trace of two matrices $A = [\begin{matrix} 2 a^{2} & 5 3 & 9 - 6 b \end{matrix}]$ and $B = [\begin{matrix} - b^{2} & 5 3 & 8 a - 8 \end{matrix}]$ are equal,where $a, b \in R,$ then $2 a - b$ equals to