Exams
Subjects
Classes
Home
Exams
Mathematics
Matrices and Determinants
if a begin bmatrix 2026 2...
Question:
medium
If \[ A= \begin{bmatrix} 2026 & 2025 & 2024 2025 & 2024 & 2023 2024 & 2023 & 2022 \end{bmatrix}, \] then \(\left|A^{2026}-A^{2025}\right|=\)
Show Hint
If any matrix factor has determinant zero, then the determinant of the product is also zero.
TS PGECET - 2026
TS PGECET
Updated On:
Jul 18, 2026
\(2026\)
\(2025\)
\(2024\)
\(0\)
Show Solution
The Correct Option is
D
Solution and Explanation
Download Solution in PDF
Was this answer helpful?
0
Top Questions on Matrices and Determinants
If \[ A = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} \] and \(\theta = \frac{2\pi}{7}\), then \(A^{100} = A \times A \times \ldots\) (100 times) is equal to:
WBJEE - 2024
Mathematics
Matrices and Determinants
View Solution
If
\[ \begin{vmatrix} x^k & x^{k+2} & x^{k+3} \\ y^k & y^{k+2} & y^{k+3} \\ z^k & z^{k+2} & z^{k+3} \end{vmatrix} = (x - y)(y - z)(z - x)\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right), \]
then the value of \(k\) is:
WBJEE - 2024
Mathematics
Matrices and Determinants
View Solution
If
\[ \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix} \cdot A \cdot \begin{pmatrix} -3 & 2 \\ 5 & -3 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \]
then \(A\) is:
WBJEE - 2024
Mathematics
Matrices and Determinants
View Solution
Let
\[ A = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ 1 & 1 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 2 \\ 1 \\ 7 \end{bmatrix}. \]
For the validity of the result \(AX = B\), \(X\) is:
WBJEE - 2024
Mathematics
Matrices and Determinants
View Solution
Want to practice more? Try solving extra ecology questions today
View All Questions
Questions Asked in TS PGECET exam
The Eigenvalues of \(3\times 3\) real matrix A are 1, 2, 3 then \(A^{-1} =\)
TS PGECET - 2026
Linear Algebra
View Solution
Let \(A=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}\). If \(u_1\) and \(u_2\) are column matrices such that \(Au_1 = \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix}\) and \(Au_2 = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}\), then \(u_1 - u_2\) is
TS PGECET - 2026
Matrices
View Solution
Let \(a,b\) and \(c\) be real numbers. Suppose there exist real numbers \(x,y,z\) which are not all zero such that the system of equations \(x = cy + bz\), \(y = cx + az\) and \(z = bx + ay\) has a non-zero solution then \(\left(a+b+c\right)^2 =\)
TS PGECET - 2026
Determinants
View Solution
For the function \(f(x)=\log x\), the number \(c\) strictly between \(e^2\) and \(e^3\) that satisfies \(f'(c)=\dfrac{f(e^3)-f(e^2)}{e^3-e^2}\) is
TS PGECET - 2026
Calculus
View Solution
The directional derivative of \(f(x,y,z)=4e^{2x-y+z}\) at the point \((1,1,-1)\) in the direction of the vector \(\vec{a}=-4\hat{i}+4\hat{j}+7\hat{k}\) is
TS PGECET - 2026
Vector Calculus
View Solution