A=\(\begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}\)if sum of diagonal elements of A13 is 3n then n equal to:
- 5
- 7
- 9
- 13
The Correct Option is B
Solution and Explanation
Top JEE Main Mathematics Questions
- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
- If , then the general value of is:
- The general solution of
- If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____
Top JEE Main Matrices Questions
Let \[ R = \begin{pmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{pmatrix} \text{ be a non-zero } 3 \times 3 \text{ matrix, where} \]
\[ x = \sin \theta, \quad y = \sin \left( \theta + \frac{2\pi}{3} \right), \quad z = \sin \left( \theta + \frac{4\pi}{3} \right) \]
and \( \theta \neq 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi \). For a square matrix \( M \), let \( \text{trace}(M) \) denote the sum of all the diagonal entries of \( M \). Then, among the statements:
- \(\text{Trace}(R) = 0\)
- If \(\text{trace}(\text{adj}(\text{adj}(R))) = 0\), then \( R \) has exactly one non-zero entry.
Which of the following is true?
- Let \( A \) be a \( 2 \times 2 \) real matrix and \( I \) be the identity matrix of order 2. If the roots of the equation \[ |A - xI| = 0 \] be \( -1 \) and \( 3 \), then the sum of the diagonal elements of the matrix \( A^2 \) is .....
- Consider the matrix \( f(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} \).
Given below are two statements:
Statement I: \( f(-x) \) is the inverse of the matrix \( f(x) \).
Statement II: \( f(x) f(y) = f(x + y) \).
In the light of the above statements, choose the correct answer from the options given below:" - Let \( A = \begin{bmatrix} 2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix} \), \( B = [B_1, B_2, B_3] \), where \( B_1, B_2, B_3 \) are column matrices, and \( AB_1 = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} \), \( AB_2 = \begin{bmatrix} 2 \\ 3 \\ 0 \end{bmatrix} \), \( AB_3 = \begin{bmatrix} 3 \\ 2 \\ 1 \end{bmatrix} \).
If \(\alpha = |B|\) and \(\beta\) is the sum of all the diagonal elements of B, then \(\alpha^3 + \beta^3\) is equal to _____. - If \( A = \begin{bmatrix} \sqrt{2} & 1 \\ -1 & \sqrt{2} \end{bmatrix} \), \( B = \begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix} \), \( C = ABA^\top \) and \( X = A^\top C^2 A \), then \( \det (X) \) is equal to:
Top JEE Main Questions
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What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
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