Let A =[x&1 1&0], x ∈ R and A 4=[ a ij ] . If a11=109, then a22 is equal to.

Question

Let A =[x&1 1&0], x ∈ R and A 4=[ a ij ] . If a11=109, then a22 is equal to. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

A=[x&1 1&0] A2 = [x&1 1&0][x&1 1&0] = [x2 +1&x x&1] A4 = [x2 +1&x x&1][x2 +1&x x&1] = [(x2+1)2 +x2&x(x2 +1) +x x(x2 +1)+x&x2 +1] a11=(x2+1)2+x2=109 ⇒ x=± 3 a22=x2+1=10

Q. Let $A = [x 1 10], x \in R$ and $A^{4} = [a_{ij}] .$ If $a_{11} = 109,$ then $a_{22}$ is equal to______.

$A = [x 1 10]$
$A^{2} = [x 1 10] [x 1 10] = [x^{2} + 1 x x 1]$
$A^{4} = [x^{2} + 1 x x 1] [x^{2} + 1 x x 1]$
$= [(x^{2} + 1)^{2} + x^{2} x (x^{2} + 1) + x x (x^{2} + 1) + x x^{2} + 1]$
$a_{11} = (x^{2} + 1)^{2} + x^{2} = 109$
$\Rightarrow x = \pm 3$
$a_{22} = x^{2} + 1 = 10$

Q. Let A=[x1​10​],x∈R and A4=[aij​]. If a11​=109, then a22​ is equal to______.

A=[x1​10​] A2=[x1​10​][x1​10​]=[x2+1x​x1​] A4=[x2+1x​x1​][x2+1x​x1​] =[(x2+1)2+x2x(x2+1)+x​x(x2+1)+xx2+1​] a11​=(x2+1)2+x2=109 ⇒x=±3 a22​=x2+1=10

Q. Let $A = [x 1 10], x \in R$ and $A^{4} = [a_{ij}] .$ If $a_{11} = 109,$ then $a_{22}$ is equal to______.

$A = [x 1 10]$
$A^{2} = [x 1 10] [x 1 10] = [x^{2} + 1 x x 1]$
$A^{4} = [x^{2} + 1 x x 1] [x^{2} + 1 x x 1]$
$= [(x^{2} + 1)^{2} + x^{2} x (x^{2} + 1) + x x (x^{2} + 1) + x x^{2} + 1]$
$a_{11} = (x^{2} + 1)^{2} + x^{2} = 109$
$\Rightarrow x = \pm 3$
$a_{22} = x^{2} + 1 = 10$