Q. What type of matrix has all its elements equal to zero? (2022)
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A.
Identity matrix
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B.
Zero matrix
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C.
Diagonal matrix
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D.
Scalar matrix
Solution
A matrix where all elements are zero is called a zero matrix.
Correct Answer:
B
— Zero matrix
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Q. What type of matrix has all its elements equal? (2022)
-
A.
Identity matrix
-
B.
Zero matrix
-
C.
Scalar matrix
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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
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Q. What type of matrix has the property A = -A? (2022)
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A.
Symmetric matrix
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B.
Skew-symmetric matrix
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C.
Identity matrix
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D.
Diagonal matrix
Solution
A skew-symmetric matrix is defined by the property A = -A.
Correct Answer:
B
— Skew-symmetric matrix
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Q. Which of the following is a characteristic of a diagonal matrix? (2022)
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A.
All elements are zero
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B.
Only diagonal elements are non-zero
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C.
All elements are equal
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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
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Q. Which of the following is a property of an identity matrix? (2019)
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A.
It is always square
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B.
It has all elements as 1
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C.
It is always a zero matrix
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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
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Q. Which of the following is a singular matrix? (2019)
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A.
[[1, 2], [3, 4]]
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B.
[[2, 3], [4, 6]]
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C.
[[5, 0], [0, 5]]
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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]]
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Q. Which of the following is a square matrix? (2020)
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A.
2x3
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B.
3x3
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C.
4x2
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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
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Q. Which of the following is a symmetric matrix? (2020)
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A.
[[1, 2], [3, 4]]
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B.
[[1, 2], [2, 1]]
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C.
[[1, 0], [0, 1]]
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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]]
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Q. Which of the following is an identity matrix? (2019)
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A.
[[1, 0], [0, 1]]
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B.
[[1, 1], [1, 1]]
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C.
[[0, 1], [1, 0]]
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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]]
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Q. Which of the following matrices is a diagonal matrix? (2023)
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A.
[[1, 0], [0, 2]]
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B.
[[1, 2], [3, 4]]
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C.
[[0, 1], [1, 0]]
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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]]
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Q. Which of the following matrices is a zero matrix? (2022)
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A.
[[0, 0], [0, 0]]
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B.
[[1, 0], [0, 1]]
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C.
[[1, 2], [3, 4]]
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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]]
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Q. Which of the following matrices is an identity matrix? (2023)
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A.
[[1, 0], [0, 1]]
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B.
[[0, 1], [1, 0]]
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C.
[[1, 1], [1, 1]]
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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]]
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Q. Which of the following matrices is an orthogonal matrix? (2021)
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A.
A matrix whose transpose is equal to its inverse
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B.
A matrix with all elements equal
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C.
A matrix with only one row
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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
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Q. Which of the following matrices is not invertible? (2019)
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A.
[[1, 2], [3, 4]]
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B.
[[0, 1], [0, 0]]
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C.
[[5, 6], [7, 8]]
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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]]
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Q. Which of the following matrices is symmetric? (2023)
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A.
A = [[1, 2], [3, 4]]
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B.
B = [[1, 2], [2, 1]]
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C.
C = [[1, 0], [0, 1]]
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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]]
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