Number of real values of for which the matrix A = [ * 20 c - 1 & … - Vidyadip

MCQ

Number of real values of $\lambda$ for which the matrix $A =$ $\left[ {\begin{array}{*{20}{c}}{\lambda - 1}&\lambda &{\lambda + 1}\\2&{ - 1}&3\\ {\lambda + 3}&{\lambda - 2}&{\lambda + 7}\end{array}} \right]$ has no inverse

A
$0$
B
$1$
C
$2$
✓
infinite

✓

Answer

Correct option: D.

infinite

d
$| A | = 0$ for all $\lambda \in R ==> A$ is singular.

Hence inverse can not be found for any value of $\lambda \in R$ ==> $(D)$

Use $R_2 \rightarrow R_2 - (R_3 - R_1)$

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