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CBSE Class 12 · 2023 · DeterminantsMultiple Choice

If

123 23 a 111

is a non-singular matrix and

a \in A

, then the set

A

is:

(A)R
(B) ${0}$
(C) ${4}$
(D) $R - {4}$ ✓ Correct

Answer: (D)

Solution

The matrix is non-singular when its determinant is non-zero. Applying

R_{2} \to R_{2} - R_{1}

,

R_{3} \to R_{3} - R_{1}

and expanding,

∣ A ∣ = a - 4

.
For non-singularity

a - 4 \neq = 0 \Rightarrow a \neq = 4

, i.e.

a \in R - {4}

.
Correct option: (D)

R - {4}

.

CBSE Class 12 Board · 2023 · Single correct option

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