For which value of k, square matrix [ cc k & 8 4 & 2 k ] is non-i… - Vidyadip

Question

For which value of $k$, square matrix $\left[\begin{array}{cc}k & 8 \\ 4 & 2 k\end{array}\right]$ is non-invertible matrix?

✓

Answer

Suppose $A=\left|\begin{array}{cc}k & 8 \\ 4 & 2 k\end{array}\right|$
A is non-invertible, then $| A |=0$
$
\begin{aligned}
\Rightarrow & & \left|\begin{array}{cc}
k & 8 \\
4 & 2 k
\end{array}\right| & =0 \\
\Rightarrow & & 2 k^2-32 & =0 \\
\Rightarrow & & k^2 & =16 \\
\Rightarrow & & k & = \pm 4
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Determinants→Determinants — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$f: Z → Z$ given by $f(x) = x^3$

Find the projection of $\vec{\text{a}}$ on $\vec{\text{b}}$ if $\vec{\text{a}}.\vec{\text{b}}=8$ and $\vec{\text{b}}=2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}.$

Integrate the function in exercise.
$\text{x} \ \sin\text{x}$

Find the equation of a line parallel to x-axis and passing through the origin.

Prove that the function $f(x) = x^3 - 6x^2 + 12x - 18$ is increasing on R.

Are the following set of ordered pairs functions? If so, examine whether the mapping is injective or surjective:
{(a, b): a is a person, b is an ancestor of a}

Find the equations of the tangent and normal to the given curves at the indicated points:
$\text{x} =\cos \text{t}, \text{y} = \sin \text{t at t}=\frac{\pi}{4} $

Simplify: $$$\cos\theta\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix} + \sin\theta\begin{bmatrix}\sin\theta&-\cos\theta\\ \cos\theta&\sin\theta\end{bmatrix}$

Write the distance of the plane $\vec{\text{r}}.(2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}})=12$ form the origin.

Evalute the following integrals:
$\int\frac{\sec\text{x}\tan\text{x}}{3\sec\text{x}+5}\text{dx}$