Q.No:1 JAM-2015
The trace of a \(2\times 2\) matrix is 4 and its determinant is 8. If one of the eigenvalues is \(2(1+i)\), the
other eigenvalue is
(A)
\(2(1-i)\)
(B)
\(2(1+i)\)
(C)
\((1+2i)\)
(D)
\((1-2i)\)
Check Answer
Option A
Q.No:2 JAM-2016
The eigenvalues of the matrix representing the following pair of linear equations
\[x+iy=0\]
\[ix+y=0\] are
(A)
\(1+i, 1+i\)
(B)
\(1-i, 1-i\)
(C)
\(1, i\)
(D)
\(1+i, 1-i\)
Check Answer
Option D
Q.No:3 JAM-2016
For the given set of equations:
\[x+y=1\]\[y+z=1\]\[x+z=1\]
which one of the following statements is correct?
(A)
Equations are inconsistent.
(B)
Equations are consistent and a single non-trivial solution exists.
(C)
Equations are consistent and many solutions exist.
(D)
Equations are consistent and only a trivial solution exists.
Check Answer
Option B
Q.No:4 JAM-2018
Let matrix \(M=\begin{pmatrix} 4&x\\ 6&9 \end{pmatrix}\). If det\((M)=0\) then,
(A)
\(M\) is symmetric.
(B)
\(M\) is invertible.
(C)
One eigenvalue is 13.
(D)
Its eigenvectors are orthogonal.
Check Answer
Option A,C,D
Q.No:5 JAM-2019
The eigenvalues of \(\begin{pmatrix} 3&i&0 \\ -i&3&0 \\ 0&0&6 \end{pmatrix}\) are
(A)
\(2,4\) and \(6\)
(B)
\(2i,4i\) and \(6\)
(C)
\(2i,4\) and \(8\)
(D)
\(0,4\) and \(8\)
Check Answer
Option A
Q.No:6 JAM-2020
If \(P\) and \(Q\) are Hermitian matrices, which of the following is/are true?
(A matrix \(P\) is Hermitian if \(P\)= \(P^\dagger\), where the elements \(P_{ij} ^\dagger =P_{ji}^*\))
(A)
\(PQ + QP\) is always Hermitian
(B)
\(i(PQ - QP)\) is always Hermitian
(C)
\(PQ\) is always Hermitian
(D)
\(PQ - QP\) is always Hermitian
Check Answer
Option A,B
Q.No:7 JAM-2021
Let \(M\) be a \(2 \times 2\) matrix. Its trace is 6 and its determinant has value 8. Its eigenvalues are
(A)
2 and 4
(B)
3 and 3
(C)
2 and 6
(D)
-2 and -3
Check Answer
Option A
Q.No:8 JAM-2022
Consider the \(2 \times 2\) matrix \(M=\begin{pmatrix} 0&a\\ a&b \end{pmatrix}\)
where \(a,b>0\). Then
(A)
\(M\) is a real symmetric matrix
(B)
One of the eigenvalues of \(M\) is greater than \(b\)
(C)
One of the eigenvalues of \(M\) is negative
(D)
Product of eigenvalues of \(M\) is \(b\)
Check Answer
Option A,B,C
Q.No:9 JAM-2023
Inverse of the matrix \(\begin{pmatrix}
1&1&0\\
2&3&0\\
1&0&1
\end{pmatrix}\)
A) \(\begin{pmatrix} 1&-2&1\\ -1&3&0\\ 0&0&1 \end{pmatrix}\)
B) \(\begin{pmatrix} 3&-1&0\\ -2&1&0\\ -3&1&1 \end{pmatrix}\)
C) \(\begin{pmatrix} -1&-1&0\\ 2&3&0\\ 1&0&1 \end{pmatrix}\)
D) \(\begin{pmatrix} 3&-2&-3\\ -2&1&1\\ 0&0&1 \end{pmatrix}\)
Check Answer
Option B
Q.No:10 JAM-2023
The sum of the eigenvalues \(\lambda_1\) and \(\lambda_2\) of matrix
\(B=I+A+A^2\), where \(A=\begin{pmatrix}2&1\\-0.5&0.5\end{pmatrix}\) is _______________ (rounded off to two decimal places).
Check Answer
Ans 7.70-7.80
Q.No:11 JAM-2024
Which of the following matrices is Hermitian as well as unitary?
A) \(\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}\)
B) \(\begin{pmatrix} 0 & i \\ i & 0 \end{pmatrix}\)
C) \(\begin{pmatrix} 1 & -i \\ i & 1 \end{pmatrix}\)
D) \(\begin{pmatrix} 0 & 1+i \\ 1-i & 0 \end{pmatrix}\)
Check Answer
Option A
Q.No:12 JAM-2025
If the system of linear equations
\[
\begin{aligned}
x + my + az &= 0 \\
2x + ay + mz &= 0 \\
ax + 2y - z &= 0
\end{aligned}
\]
with \(m\) and \(a\) as non-zero constants, admits a non-trivial solution,
then which one of the following conditions is correct?
A) \(m^2 - a^2 = 3\)
B) \(m^2 - a^2 = -3\)
C) \(a^2 - 2m^2 = -3\)
D) \(m^2 - 2a^2 = 3\)