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CUET (PG)
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Mathematics
List of top Mathematics Questions on Linear Algebra asked in CUET (PG)
What is the order of the group of permutations \( S_3 \)?
CUET (PG) - 2026
CUET (PG)
Mathematics
Linear Algebra
What are the possible values for the rank of a \(4 \times 3\) matrix?
CUET (PG) - 2026
CUET (PG)
Mathematics
Linear Algebra
What is the condition for a group \( G \) to be Abelian based on the commutator subgroup?
CUET (PG) - 2026
CUET (PG)
Mathematics
Linear Algebra
If \( T: V \to W \) is a linear transformation, what is the relationship between rank(\(T\)), nullity(\(T\)), and dim(\(V\))?
CUET (PG) - 2026
CUET (PG)
Mathematics
Linear Algebra
If \( A \) is a \(3 \times 3\) matrix with eigenvalues \(1, 2, 3\), what is the determinant of \(A^2\)?
CUET (PG) - 2026
CUET (PG)
Mathematics
Linear Algebra
How many elements of order 5 are there in a cyclic group of order 25?
CUET (PG) - 2026
CUET (PG)
Mathematics
Linear Algebra
What is the dimension of the vector space of all \( n \times n \) real symmetric matrices?
CUET (PG) - 2026
CUET (PG)
Mathematics
Linear Algebra
If the matrix \[ A = \begin{pmatrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{pmatrix} \] satisfies the matrix equation:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
The roots of the equation \( x^4 - 20x^3 + 140x^2 - 400x + 384 = 0 \) are in
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
If the rank of matrix \[ \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 0 & 7 & \lambda \end{pmatrix} \] is 2, then the value of \(\lambda\) is:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
The system of equations
x + 2y + z = 6
x + 4y + 3z = 10
x + 4y + \(\lambda\)z = \(\mu\)
is inconsistent if
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
Which of the following statements are correct?
If \[ A = \begin{pmatrix} p & q \\ 0 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & q \\ 0 & 1 \end{pmatrix}, \] then
(A) \[ B^n = \begin{pmatrix} 1 & nq \\ 0 & 1 \end{pmatrix} \]
(B) \[ A^n = \begin{pmatrix} p^n & q\frac{p^n-1}{p-1} \\ 0 & 1 \end{pmatrix}, \; \text{if } p \neq 1 \]
(C) \[ AB = \begin{pmatrix} p & pq+q \\ 0 & 1 \end{pmatrix} \]
(D) \[ B^{n-1} = \begin{pmatrix} 1 & (n+1)q \\ 0 & 1 \end{pmatrix} \]
(E) \[ AB^n = \begin{pmatrix} p & (np+1)q \\ 0 & 1 \end{pmatrix} \]
Choose the correct answer from the options given below:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
Let V(F) be a finite dimensional vector space and T: V \(\to\) V be a linear transformation. Let R(T) denote the range of T and N(T) denote the null space of T. If rank(T) = rank(T\textsuperscript{2}), then which of the following are correct?
A. N(T) = R(T)
B. N(T) = N(T\textsuperscript{2})
C. N(T) \(\cap\) R(T) = \{0\
D. R(T) = R(T\textsuperscript{2})}
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
Let \(m, n \in \mathbb{N}\) such that \(m<n\) and \(P_{m \times n}(\mathbb{R})\) and \(Q_{n \times m}(\mathbb{R})\) are matrices over real numbers and let \(\rho(V)\) denotes the rank of the matrix V. Then, which of the following are NOT possible.
A. \( \rho(PQ) = n \)
B. \( \rho(QP) = m \)
C. \( \rho(PQ) = m \)
D. \( \rho(QP) = \lfloor(m+n)/2\rfloor \), where \(\lfloor \rfloor\) is the greatest integer function
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
Which of the following are subspaces of vector space \(\mathbb{R}^3\):
A. \( \{(x,y,z) : x+y=0\ \)
B. \( \{(x,y,z) : x-y=0\} \)
C. \( \{(x,y,z) : x+y=1\} \)
D. \( \{(x,y,z) : x-y=1\} \)}
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
If \( A = \begin{pmatrix} 2 & 4 & 1 \\ 0 & 2 & -1 \\ 0 & 0 & 1 \end{pmatrix} \) satisfies \( A^3 + \mu A^2 + \lambda A - 4I_3 = 0 \), then the respective values of \( \lambda \) and \( \mu \) are:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
Let A and B be two symmetric matrices of same order, then which of the following statement are correct:
A. AB is symmetric
B. A+B is symmetric
C. \( A^T B = AB^T \)
D. \( BA = (AB)^T \)
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
The number of maximum basic feasible solution of the system of equations AX = b, where A is m \( \times \) n matrix, b is n \( \times \) 1 column matrix and rank of A is \(\rho(A) = m\), is:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
If the vectors \( \begin{pmatrix} 1 \\ -1 \\ 3 \end{pmatrix}, \begin{pmatrix} 1 \\ 2 \\ -3 \end{pmatrix}, \begin{pmatrix} p \\ 0 \\ 1 \end{pmatrix} \) are linearly dependent, then the value of p is:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
The system of linear equations \( x+y+z=6 \), \( x+2y+5z=10 \), \( 2x+3y+\lambda z=\mu \) has a unique solution, if
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
Let A be a \( 2 \times 2 \) matrix with \( \det(A) = 4 \) and \( \text{trace}(A) = 5 \). Then the value of \( \text{trace}(A^2) \) is:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
Which of the following set of vectors forms the basis for \( \mathbb{R}^3 \)?
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
If U and W are distinct 4-dimensional subspaces of a vector space V of dimension 6, then the possible dimensions of \( U \cap W \) is:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra
Which of the following forms a linear transformation:
CUET (PG) - 2025
CUET (PG)
Mathematics
Linear Algebra