Exams › JEE Main › Maths

If [1 ω ω^2; ω ω^2 1; ω^2 1 ω] [k 1 1; 1 1 1; 1 1 1] = [0 0 0; 0 0 0; 0 0 0], then the value of k is

1. 6
2. 1
3. 8
4. 9

Correct answer: 8

Solution

The correct option is 8 because the matrix multiplication results in a zero matrix only when the determinant of the first matrix is zero, which occurs at k = 8, satisfying the condition for the linear dependence of the rows.

Related JEE Main Maths questions

• If $A$ is a square matrix, then the matrix product $AA^T$ is a
• Let $f(\alpha)=\begin{bmatrix}\cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha\end{bmatrix}$. If $\alpha$, $\beta$, and $\gamma$ are the angles of a triangle, then the product $f(\alpha)f(\beta)f(\gamma)$ is equal to
• Let $A$, $B$, and $C$ be $n\times n$ matrices. Which of the following statements is true?
• Given the matrix $A_\alpha=\begin{bmatrix}\cos\alpha & -\sin\alpha\\ \sin\alpha & \cos\alpha\end{bmatrix}$, which of the following identities is true?
• Let $A$ be a square matrix satisfying $(A-2I)(A+I)=O$. Then $A^{-1}$ equals:
• A square matrix $P$ obeys the relation $P^2=I-P$, where $I$ denotes the identity matrix. If $P^n=5I-8P$, then the value of $n$ is

⚔️ Practice JEE Main Maths free + battle 1v1 →