MTH501 Final Term MCQs 2026 by VUBuddy

Q1. If a vector space V has a basis of n vectors then every basis of V must consists of exactly --------

1. n vectors
2. n-1 vectors
3. n+1 vectors
4. n+2 vectors

Correct answer: n vectors

Q2. The determinant of identity matrix is?

1. 0
2. None of the mentioned
3. Depends on the matrix
4. 1

Correct answer: 1

Q3. If a vector space V has a basis B={b_1, b_2, …, b_n} then any set in V, containing more than n vectors, must be -----------

1. Linearly dependent
2. Linearly Independent

Correct answer: Linearly dependent

Q4. A set of two non-zero vectors are linearly independent if and only if they are --------------- to/of each other.

1. Scalar multiple
2. Equal

Correct answer: Scalar multiple

Q5. The vectors spaces F(-\infty, +\infty) and C(-\infty, +\infty) are ----------

1. Infinite-dimensional
2. Finite-dimensional

Correct answer: Infinite-dimensional

Q6. The act of changing A into P^-1 AP is called a similarity transformation

1. False
2. True

Correct answer: True

Q7. The point of intersection of axes in three dimension coordinates system is called?

1. Ordinate
2. Collective intercept
3. Collective coordinate
4. Parallel pair order

Correct answer: Ordinate

Q8. Rank of the matrix A=\left[ \begin{gathered} 0\,\,\,0\,\,\,0\,\,\,0 \hfill \\ 4\,\,\,6\,\,\,\,1\,\,\,\,0\, \hfill \\ 1\,\,\,\,\,0\,\,\,\,0\,\,\,\,0 \hfill \\\ \end{gathered} \right]

1. 3
2. 0
3. 2
4. 1

Correct answer: 2

Q1. If one of the Eigenvalues of {\left[ A \right]_{n \times n}} is zero, it implies

1. The solution to [A][X]=[C] system of equations is unique
2. The determinant of [A] is zero
3. The solution to [A][X]=[0]
4. The determinant of [A] is nonzero

Correct answer: The determinant of [A] is zero

Q2. If A and B are n x n matrices, then det (AB) = ______________.

1. det(A).det(B)
2. det(B)
3. B
4. det(A).B

Correct answer: det(A).det(B)

Q3. Let A be n x n matrix, then A is invertible if and only if

1. det A is zero
2. det A is not zero

Correct answer: det A is not zero

Q4. An n x n matrix A is diagonalizable if and only if A has ____ linearly independent eigenvectors.

1. n - 1
2. n
3. n + 1
4. n x n

Correct answer: n

Q5. {\rm{If}}\,{\rm{AB = I = BA \,\ for }}\,\ matrices{\rm{ }}A,\,B\;and\,I,{\rm{ }}where\;\,I\,is\,\ an \,\ identity \,\ matrix, \,\ then

1. A is inverse of B,
2. B is inverse of A,
3. All of the above.
4. {A^{( - 1)}} = B,{B^{( - 1)}} = A,

Correct answer: All of the above.

Q6. Let A be a real 2 by 2 matrix with complex eigen values \lambda=a-b+{i}, (b\neq 0) and associated eigenvectors v in C^2, then A=PCP^{-1}, where P=--------------

1. P=[Rev -Imv]
2. P=[-Rev -Imv]
3. P=[Rev Imv]
4. P=[-Rev Imv]

Correct answer: P=[Rev Imv]

Q7. A null space is a vector space.

1. False
2. True

Correct answer: True

Q8. Every square matrix A has at least one ----------.

1. Critical point
2. Fixed point

Correct answer: Fixed point

Q9. We can add the matrices of ______________.

1. same order
2. same number of rows
3. same number of columns
4. different order

Correct answer: same order

Q10. Let A be an n by n matrix whose distinct eigen values are \lambda_{1}, \lambda_{2},…, \lambda_{p}. For 1 \leq k \leq p, the dimension of the eigen space for \lambda_{k} is -------- than or ------- to the multiplicity of the eigen value \lambda_{k}

1. Less, equal
2. Greater, equal

Correct answer: Less, equal