Question:
Find the sum of eigenvalues of the matrix: \( \begin{bmatrix} 4 & 1 \\ 3 & 6 \end{bmatrix} \)
Find the sum of eigenvalues of the matrix: \( \begin{bmatrix} 4 & 1 \\ 3 & 6 \end{bmatrix} \)
Show Hint
Sum of eigenvalues is the trace of the matrix.
Updated On: Dec 22, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 10
Solution and Explanation
Eigenvalue sum = trace of matrix:
\[
\text{trace} = 4 + 6 = 10
\]
Was this answer helpful?
0
0
Top Questions on Eigenvalues and Eigenvectors
For the matrix, $A = \begin{bmatrix} -4 & 0 \\ -1.6 & 4 \end{bmatrix}$, the eigenvalues ($\lambda$) and eigenvectors ($X$) respectively are:
- CUET (PG) - 2025
- Civil Structural and Transport Engineering
- Eigenvalues and Eigenvectors
- The eigen value corresponding to the eigen vector \(\begin{bmatrix} 1 \\ 2 \end{bmatrix}\) for the matrix \(\begin{bmatrix} 4 & 2 \\ 2 & 4 \end{bmatrix}\) is:
- CUET (PG) - 2025
- Chemical, Thermal and Polymer Engineering
- Eigenvalues and Eigenvectors
- Let \( M = (m_{ij}) \) be a \( 3 \times 3 \) real, invertible matrix and \( \sigma \in S_3 \) be the permutation defined by \( \sigma(1) = 2, \sigma(2) = 3 \) and \( \sigma(3) = 1 \). The matrix \( M_\sigma \) is defined by \( n_{ij} = m_{i\sigma(j)} \) for all \( i,j \in \{1, 2, 3\} \). Then, which one of the following is TRUE?
- IIT JAM MA - 2025
- Mathematics
- Eigenvalues and Eigenvectors
- Let \[ M = \begin{pmatrix} 2 & 0 & -1 \\ 4 & 1 & -4 \\ 2 & 0 & x \end{pmatrix} \] for some real number \( x \).
If \( 0 \) is an eigenvalue of \( M \), then \[ (M^4 + M) \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} \] is equal to- IIT JAM MA - 2025
- Mathematics
- Eigenvalues and Eigenvectors
- Let \[ M = \begin{pmatrix} 6 & 2 & -6 & 8 \\ 5 & 3 & -9 & 8 \\ 3 & 1 & -2 & 4 \end{pmatrix} \] Consider the system \( S \) of linear equations given by:
\[ 6x_1 + 2x_2 - 6x_3 + 8x_4 = 8 \] \[ 5x_1 + 3x_2 - 9x_3 + 8x_4 = 16 \] \[ 3x_1 + x_2 - 2x_3 + 4x_4 = 32 \] where \( x_1, x_2, x_3, x_4 \) are unknowns.
Then, which one of the following is TRUE?- IIT JAM MA - 2025
- Mathematics
- Eigenvalues and Eigenvectors
View More Questions
Questions Asked in GATE AG exam
- The series \[ \sum_{n=0}^{r} q^n = 1 + q + q^2 + \cdots + q^r \] has the sum:
- GATE AG - 2025
- geometric progression
- If \(a\), \(b\), and \(c\) are the roots of \( 2x^3 - 3x^2 + px - 1 = 0 \) and the sum of two roots is 1, the value of \(p\) is:
- GATE AG - 2025
- Algebraic Methods of Solving a Pair of Linear Equations
- While sowing mustard seeds (bulk density = 800 kg.m\(^{-3}\)), a four-row fluted roller type seed drill with 25 cm row spacing operates at a speed of 2.5 km.h\(^{-1}\). For a desired seed rate of 5.0 kg.ha\(^{-1}\), the flowrate of seeds from the machine in m\(^3\).h\(^{-1}\) is:
- GATE AG - 2025
- Soil Mechanics
- The average marks obtained by a class in an examination were calculated as 30.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 24 instead of 42. After correcting the marks, the average becomes 31.4. How many students does the class have?
Consider the relationships among P, Q, R, S, and T:
• P is the brother of Q.
• S is the daughter of Q.
• T is the sister of S.
• R is the mother of Q.
The following statements are made based on the relationships given above.
(1) R is the grandmother of S.
(2) P is the uncle of S and T.
(3) R has only one son.
(4) Q has only one daughter.
Which one of the following options is correct?- GATE MA - 2025
- GATE AG - 2025
- Blood Relations
View More Questions