Q. What is the trace of the matrix H = [[2, 0, 1], [0, 3, 0], [1, 0, 4]]? (2019)
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(H) = 2 + 3 + 4 = 9.
Correct Answer:
C
— 7
Learn More →
Q. What is the trace of the matrix H = [[2, 1], [1, 3]]?
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(H) = 2 + 3 = 5.
Correct Answer:
B
— 4
Learn More →
Q. What is the trace of the matrix I = [[3, 2], [1, 4]]? (2023)
Solution
The trace of a matrix is the sum of its diagonal elements. Here, trace(I) = 3 + 4 = 7.
Correct Answer:
B
— 6
Learn More →
Q. What is the trace of the matrix I = [[5, 2], [3, 4]]? (2022)
Solution
The trace of a matrix is the sum of its diagonal elements. Thus, trace(I) = 5 + 4 = 9.
Correct Answer:
C
— 9
Learn More →
Q. What is the value of the determinant of the matrix G = [[1, 2, 3], [0, 1, 4], [5, 6, 0]]? (2022)
Solution
Using the determinant formula, det(G) = 1(1*0 - 4*6) - 2(0 - 4*5) + 3(0 - 1*5) = -24 + 40 - 15 = 1.
Correct Answer:
A
— -34
Learn More →
Q. What is the value of x if the matrix A = [[x, 2], [3, 4]] is singular?
Solution
A matrix is singular if its determinant is zero. Det(A) = (x*4) - (2*3) = 4x - 6 = 0. Solving gives x = 1.5.
Correct Answer:
C
— 3
Learn More →
Q. What is the volume of a cube with a side length of 5 cm? (2022)
-
A.
25 cm³
-
B.
50 cm³
-
C.
125 cm³
-
D.
150 cm³
Solution
The volume of a cube is given by V = side³. For a side length of 5 cm, V = 5³ = 125 cm³.
Correct Answer:
C
— 125 cm³
Learn More →
Q. What type of matrix has all its diagonal elements as 1 and all other elements as 0? (2023)
-
A.
Identity matrix
-
B.
Zero matrix
-
C.
Diagonal matrix
-
D.
Scalar matrix
Solution
An identity matrix is defined as a square matrix with all diagonal elements equal to 1 and all other elements equal to 0.
Correct Answer:
A
— Identity matrix
Learn More →
Q. What type of matrix has all its elements equal to zero? (2022)
-
A.
Identity matrix
-
B.
Zero matrix
-
C.
Diagonal matrix
-
D.
Scalar matrix
Solution
A matrix where all elements are zero is called a zero matrix.
Correct Answer:
B
— Zero matrix
Learn More →
Q. What type of matrix has all its elements equal? (2022)
-
A.
Identity matrix
-
B.
Zero matrix
-
C.
Scalar matrix
-
D.
Diagonal matrix
Solution
A scalar matrix is a square matrix in which all the elements are equal to the same scalar value.
Correct Answer:
C
— Scalar matrix
Learn More →
Q. What type of matrix has the property A = -A? (2022)
-
A.
Symmetric matrix
-
B.
Skew-symmetric matrix
-
C.
Identity matrix
-
D.
Diagonal matrix
Solution
A skew-symmetric matrix is defined by the property A = -A.
Correct Answer:
B
— Skew-symmetric matrix
Learn More →
Q. Which of the following is a characteristic of a diagonal matrix? (2022)
-
A.
All elements are zero
-
B.
Only diagonal elements are non-zero
-
C.
All elements are equal
-
D.
It is always square
Solution
A diagonal matrix has non-zero elements only on its diagonal, while all off-diagonal elements are zero.
Correct Answer:
B
— Only diagonal elements are non-zero
Learn More →
Q. Which of the following is a property of an identity matrix? (2019)
-
A.
It is always square
-
B.
It has all elements as 1
-
C.
It is always a zero matrix
-
D.
It has a determinant of 0
Solution
An identity matrix is always square and has 1s on the diagonal and 0s elsewhere.
Correct Answer:
A
— It is always square
Learn More →
Q. Which of the following is a singular matrix? (2019)
-
A.
[[1, 2], [3, 4]]
-
B.
[[2, 3], [4, 6]]
-
C.
[[5, 0], [0, 5]]
-
D.
[[0, 1], [1, 0]]
Solution
A singular matrix is one that does not have an inverse, which occurs when its determinant is zero. The matrix [[2, 3], [4, 6]] is singular.
Correct Answer:
B
— [[2, 3], [4, 6]]
Learn More →
Q. Which of the following is a square matrix? (2020)
-
A.
2x3
-
B.
3x3
-
C.
4x2
-
D.
5x1
Solution
A square matrix is one where the number of rows is equal to the number of columns. Among the options, only 3x3 has equal rows and columns.
Correct Answer:
B
— 3x3
Learn More →
Q. Which of the following is a symmetric matrix? (2020)
-
A.
[[1, 2], [3, 4]]
-
B.
[[1, 2], [2, 1]]
-
C.
[[1, 0], [0, 1]]
-
D.
[[0, 1], [1, 0]]
Solution
A symmetric matrix is one that is equal to its transpose. The matrix [[1, 2], [2, 1]] is symmetric.
Correct Answer:
B
— [[1, 2], [2, 1]]
Learn More →
Q. Which of the following is an identity matrix? (2019)
-
A.
[[1, 0], [0, 1]]
-
B.
[[1, 1], [1, 1]]
-
C.
[[0, 1], [1, 0]]
-
D.
[[2, 0], [0, 2]]
Solution
An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. The matrix [[1, 0], [0, 1]] fits this definition.
Correct Answer:
A
— [[1, 0], [0, 1]]
Learn More →
Q. Which of the following matrices is a diagonal matrix? (2023)
-
A.
[[1, 0], [0, 2]]
-
B.
[[1, 2], [3, 4]]
-
C.
[[0, 1], [1, 0]]
-
D.
[[1, 1], [1, 1]]
Solution
A diagonal matrix is one where all off-diagonal elements are zero. The matrix [[1, 0], [0, 2]] is a diagonal matrix.
Correct Answer:
A
— [[1, 0], [0, 2]]
Learn More →
Q. Which of the following matrices is a zero matrix? (2022)
-
A.
[[0, 0], [0, 0]]
-
B.
[[1, 0], [0, 1]]
-
C.
[[1, 2], [3, 4]]
-
D.
[[0, 1], [1, 0]]
Solution
A zero matrix is one where all elements are zero. The matrix [[0, 0], [0, 0]] meets this criterion.
Correct Answer:
A
— [[0, 0], [0, 0]]
Learn More →
Q. Which of the following matrices is an identity matrix? (2023)
-
A.
[[1, 0], [0, 1]]
-
B.
[[0, 1], [1, 0]]
-
C.
[[1, 1], [1, 1]]
-
D.
[[0, 0], [0, 0]]
Solution
An identity matrix has 1s on the diagonal and 0s elsewhere. The matrix [[1, 0], [0, 1]] fits this definition.
Correct Answer:
A
— [[1, 0], [0, 1]]
Learn More →
Q. Which of the following matrices is an orthogonal matrix? (2021)
-
A.
A matrix whose transpose is equal to its inverse
-
B.
A matrix with all elements equal
-
C.
A matrix with only one row
-
D.
A matrix with all diagonal elements equal
Solution
An orthogonal matrix is defined as a matrix whose transpose is equal to its inverse.
Correct Answer:
A
— A matrix whose transpose is equal to its inverse
Learn More →
Q. Which of the following matrices is not invertible? (2019)
-
A.
[[1, 2], [3, 4]]
-
B.
[[0, 1], [0, 0]]
-
C.
[[5, 6], [7, 8]]
-
D.
[[9, 10], [11, 12]]
Solution
A matrix is not invertible if its determinant is zero. The matrix [[0, 1], [0, 0]] has a determinant of 0.
Correct Answer:
B
— [[0, 1], [0, 0]]
Learn More →
Q. Which of the following matrices is symmetric? (2023)
-
A.
A = [[1, 2], [3, 4]]
-
B.
B = [[1, 2], [2, 1]]
-
C.
C = [[1, 0], [0, 1]]
-
D.
D = [[1, 2, 3], [4, 5, 6]]
Solution
A symmetric matrix is one that is equal to its transpose. Matrix B is symmetric because B = B^T.
Correct Answer:
B
— B = [[1, 2], [2, 1]]
Learn More →
Showing 91 to 113 of 113 (4 Pages)
