Let A be a non-singular matrix and X- 0- Y- 0 be two column matrices such that AX - 1100X and A-1Y - - Y- find one of the possible values of -

Given #160;AX= 1 100 X ⇒ A= 1 100 I #160; #160;....(1)Also given A ^ 1 Y=λ Y IY=λ AY #160; #160; #160; #160; #16 ...

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Standard XII

Mathematics

Inverse of a Matrix

Let A be a ...

Question

Let $A$ be a non-singular matrix and $X \neq 0, Y \neq 0$ be two column matrices such that $A X = (\frac{1}{100}) X a n d A^{- 1} Y = λ Y$ , find one of the possible values of $λ$ .

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Solution

Given $A X = \frac{1}{100} X$
$\Rightarrow A = \frac{1}{100} I$ ....(1)
Also given $A^{- 1} Y = λ Y$
$I Y = λ A Y$ (Multiplying by A to both sides)
$Y = λ \frac{1}{100} Y$
$\Rightarrow 100 Y = λ Y$
$\Rightarrow λ = 100$

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Let A be a non-singular matrix and X≠0,Y≠0 be two column matrices such that AX=(1100)XandA−1Y=λY, find one of the possible values of λ.

Given AX=1100X⇒A=1100I ....(1)Also given A−1Y=λYIY=λAY (Multiplying by A to both sides)Y=λ1100Y⇒100Y=λY⇒λ=100

Let $A$ be a non-singular matrix and $X \neq 0, Y \neq 0$ be two column matrices such that $A X = (\frac{1}{100}) X a n d A^{- 1} Y = λ Y$ , find one of the possible values of $λ$ .

Given $A X = \frac{1}{100} X$
$\Rightarrow A = \frac{1}{100} I$ ....(1)
Also given $A^{- 1} Y = λ Y$
$I Y = λ A Y$ (Multiplying by A to both sides)
$Y = λ \frac{1}{100} Y$
$\Rightarrow 100 Y = λ Y$
$\Rightarrow λ = 100$