Let A be a non-singular matrix and X=0,Y=0 be two column matrices such that AX=(1001)XandA−1Y=λY, find one of the possible values of λ.

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Let A be a non-singular matrix and X 0, :Y 0 be two column mat

Question

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

100

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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 an d A^{- 1} Y = λY

, find one of the possible values of

λ

7 mins ago

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7 mins ago

Given

A X = \frac{1}{100} X

\Rightarrow A = \frac{1}{100} I

....(1)

Also given

A^{- 1} Y = λY

I Y = λ A Y

(Multiplying by A to both sides)

Y = λ \frac{1}{100} Y

\Rightarrow 100 Y = λY

\Rightarrow λ = 100

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Question Text	Let $A$ be a non-singular matrix and $X \neq = 0, Y \neq = 0$ be two column matrices such that $A X = (\frac{1}{100}) X an d A^{- 1} Y = λY$ , find one of the possible values of $λ$ .
Answer Type	Text solution:1
Upvotes	150