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CBSE Class 12 · 2019 · MatricesShort Answer

If

A = [4 - 1 21]

, show that

(A - 2 I) (A - 3 I) = 0

.

Answer: Proved

Solution

Form the two factor matrices.

A - 2 I = [2 - 1 2 - 1], A - 3 I = [1 - 1 2 - 2] .

Multiply them:

(A - 2 I) (A - 3 I) = [2 - 1 2 - 1] [1 - 1 2 - 2] = [2 - 2 - 1 + 1 4 - 4 - 2 + 2] = [0000] .

Hence

(A - 2 I) (A - 3 I) = 0

. Proved. (Equivalently,

2

and

3

are the eigenvalues of

A

.)

CBSE Class 12 Board · 2019 · Subjective

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