If 3A -1 -2 -2 2 1 -2 x -2 y T such that A AT - I- then which of the following are correct -

The correct options are B x + 2y = 4 C x y = 1 D x^2 + y^2 = 5 3A . 3A^T = 1 amp; 2 amp;x 2 amp;1 nbsp; amp; 2 ...

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Byju's Answer

Standard XII

Mathematics

Multiplication of Matrices

If 3A =-1 ...

Question

If $3 A = {∣ ∣ ∣ ∣ \begin{matrix} - 1 & - 2 & - 2 2 & 1 & - 2 x & - 2 & y \end{matrix} ∣ ∣ ∣ ∣}^{T}$ such that $A A^{T} = I$ , then which of the following are correct ?

x + 2 y = 4

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x - y = 1

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x^{2} + y^{2} = 3

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x^{2} + y^{2} = 5

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Solution

The correct options are
B $x + 2 y = 4$
C $x - y = 1$
D $x^{2} + y^{2} = 5$
$3 A . 3 A^{T} = ∣ ∣ ∣ ∣ \begin{matrix} - 1 & 2 & x - 2 & 1 & - 2 - 2 & - 2 & y \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} - 1 & - 2 & - 2 2 & 1 & - 2 x & - 2 & y \end{matrix} ∣ ∣ ∣ ∣$
$= ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + 4 + x^{2} & 2 + 2 - 2 x & 2 - 4 + x y 2 + 2 - 2 x & 4 + 1 + 4 & 4 - 2 - 2 y 2 - 4 + x y & 4 - 2 - 2 y & 4 + 4 + y^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} 9 & 0 & 0 0 & 9 & 0 0 & 0 & 9 \end{matrix} ∣ ∣ ∣ ∣$
( $∵ A A^{T} = I$ )
$∴ 5 + x^{2} = 9, 4 - 2 x = 0, 4 - 2 - 2 y = 0, x y = 2$
$i . e . x = 2, y = 1$

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If 3A=∣∣ ∣∣−1−2−221−2x−2y∣∣ ∣∣T such that AAT=I, then which of the following are correct ?

If $3 A = {∣ ∣ ∣ ∣ \begin{matrix} - 1 & - 2 & - 2 2 & 1 & - 2 x & - 2 & y \end{matrix} ∣ ∣ ∣ ∣}^{T}$ such that $A A^{T} = I$ , then which of the following are correct ?