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
- Which plant hormone is mainly responsible for apical dominance?
- GATE AG - 2026
- Plant Growth Regulators
- Which nutrient is most commonly deficient in Indian soils?
- GATE AG - 2026
- Soil Mechanics
- The duty of water is defined as:
- GATE AG - 2026
- Soil Mechanics
- The efficiency of irrigation system is maximum in:
- GATE AG - 2026
- Soil Mechanics
- Which one of the following crops is most sensitive to photoperiod?
- GATE AG - 2026
- Cropping System
View More Questions