(A) Given the matrix $A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}$.First,calculate the determinant of $A$:$|A| = \alpha^2 - (2 \times 2

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) Given the matrix $A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}$.First,calculate the determinant of $A$:$|A| = \alpha^2 - (2 \times 2) = \alpha^2 - 4$.We are given that $|A^3| = 125$.Using the property of determinants $|A^n| = |A|^n$,we have $|A|^3 = 125$.Taking the cube root on both sides,we get $|A| = \sqrt[3]{125} = 5$.Now,substitute the value of $|A|$ back into the equation:$\alpha^2 - 4 = 5$.$\alpha^2 = 9$.$\alpha = \pm 3$.Therefore,the correct option is $A$.

Class 12 Mathematics 3-4. Matrices and Determinants Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

Easy

If $A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}$ and $|A^3| = 125$,then $\alpha = $ . . . . . .

GSEB 2016 All GSEB

A
$\pm 3$
B
$\pm 2$
C
$\pm 1$
D
$\pm 5$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

3-4. Matrices and Determinants

Subtopic

Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

Previous Year

GSEB 2016 Paper All GSEB years →

If ${\left| {\begin{array}{cc} 4 & 1 \\ 2 & 1 \end{array}} \right|^2} = \left| {\begin{array}{cc} 3 & 2 \\ 1 & x \end{array}} \right| - \left| {\begin{array}{cc} x & 3 \\ -2 & 1 \end{array}} \right|$,then $x =$

Medium

View Solution

What is the area of the triangle formed by the points $(a, b + c)$,$(b, c + a)$,and $(c, a + b)$?

Easy

View Solution

$\left|\begin{array}{lll}24 & 25 & 26 \\ 25 & 26 & 27 \\ 26 & 27 & 27\end{array}\right|$ is equal to

EasyAP EAMCET 2011

View Solution

If $a, b, c$ are positive and not all equal,then the value of the determinant $\left| \begin{array}{ccc} a & b & c \\ b & c & a \\ c & a & b \end{array} \right|$ is

MediumIIT 1982

View Solution

The area of a triangle with vertices $(-3, 0)$, $(3, 0)$, and $(0, k)$ is $9$ sq units. Find the possible values of $k$.

DifficultKCET 2023

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $A = \begin{bmatrix} \alpha & 2 \\ 2 & \alpha \end{bmatrix}$ and $|A^3| = 125$,then $\alpha = $ . . . . . .

Similar Questions

If ${\left| {\begin{array}{cc} 4 & 1 \\ 2 & 1 \end{array}} \right|^2} = \left| {\begin{array}{cc} 3 & 2 \\ 1 & x \end{array}} \right| - \left| {\begin{array}{cc} x & 3 \\ -2 & 1 \end{array}} \right|$,then $x =$

What is the area of the triangle formed by the points $(a, b + c)$,$(b, c + a)$,and $(c, a + b)$?

$\left|\begin{array}{lll}24 & 25 & 26 \\ 25 & 26 & 27 \\ 26 & 27 & 27\end{array}\right|$ is equal to

If $a, b, c$ are positive and not all equal,then the value of the determinant $\left| \begin{array}{ccc} a & b & c \\ b & c & a \\ c & a & b \end{array} \right|$ is

The area of a triangle with vertices $(-3, 0)$, $(3, 0)$, and $(0, k)$ is $9$ sq units. Find the possible values of $k$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module