If 514762135 16-7 62 4-74 3571163425^2020= a_1 a_2 a_3 b_1 b_2 b_3 c_1 c_2 c_3 , then the value of 2a_2-b_1+3a_3-c_1+4b_3-c_2 is equal to

Correct answer: (A) 0. Let, X=ABA^T2020 ( ∵ B is symmetric) X^T=ABA^T2020T=ABA^TT2020=ABA^T2020 X=X^T⇒X is a symmetric matrix ⇒a_2=b_1,a_3=c_1,b_3=c_2 ⇒ Required value =0

Q32 / 75 · NTA Abhyas (JEE Main) 2020 · Mathematics · Matrices

If ${\{[\begin{array}{l} 5 & 1 & 4 \\ 7 & 6 & 2 \\ 1 & 3 & 5 \end{array}] [\begin{array}{l} 1 & 6 & - 7 \\ 6 & 2 & 4 \\ - 7 & 4 & 3 \end{array}] [\begin{array}{l} 5 & 7 & 1 \\ 1 & 6 & 3 \\ 4 & 2 & 5 \end{array}]\}}^{2020} =$ $[\begin{array}{l} a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3} \end{array}]$ , then the value of $2 |a_{2} - b_{1}| + 3 |a_{3} - c_{1}| + 4 |b_{3} - c_{2}|$ is equal to

Correct answer
A
$0$
B
$1$
C
$2$
D
$3$

Solution

Let,

X = {(A B A^{T})}^{2020}

(

∵

B

is symmetric)

X^{T} = {({(A B A^{T})}^{2020})}^{T} = {({(A B A^{T})}^{T})}^{2020} = {(A B A^{T})}^{2020}

X = X^{T} \Rightarrow X

is a symmetric matrix

\Rightarrow a_{2} = b_{1}, a_{3} = c_{1}, b_{3} = c_{2}

\Rightarrow

Required value

= 0

Hence, the correct answer is option: 'A'.

If 514762135 16-7 62 4-74 35711634252020=a1a2a3b1b2b3c1c2c3, then the value of 2a2-b1+3a3-c1+4b3-c2 is equal to

Solution

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