Types of Matrices
Q. If A is a 2x2 matrix and B is a 2x3 matrix, what is the order of the product AB? (2019)
A.
2x2
B.
2x3
C.
3x2
D.
2x5
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Solution
The order of the product of two matrices is determined by the outer dimensions. Here, A (2x2) and B (2x3) can be multiplied, resulting in a matrix of order 2x3.
Correct Answer: B — 2x3
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Q. If A is a 3x3 matrix, how many elements does it have? (2023)
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Solution
A 3x3 matrix has 3 rows and 3 columns, resulting in a total of 3 * 3 = 9 elements.
Correct Answer: B — 9
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Q. If a matrix is diagonal, what can be said about its non-diagonal elements? (2020)
A.
They are all zero
B.
They are all one
C.
They can be any value
D.
They are negative
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Solution
In a diagonal matrix, all non-diagonal elements are zero.
Correct Answer: A — They are all zero
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Q. What is the determinant of a 2x2 matrix A = [[a, b], [c, d]]? (2021)
A.
ad - bc
B.
ab + cd
C.
ac + bd
D.
ad + bc
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Solution
The determinant of a 2x2 matrix is calculated as ad - bc.
Correct Answer: A — ad - bc
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Q. What is the order of a matrix with 3 rows and 4 columns? (2021)
A.
3x4
B.
4x3
C.
3x3
D.
4x4
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Solution
The order of a matrix is given by the number of rows followed by the number of columns. Therefore, a matrix with 3 rows and 4 columns is of order 3x4.
Correct Answer: A — 3x4
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Q. What is the trace of a square matrix? (2022)
A.
Sum of all elements
B.
Product of diagonal elements
C.
Sum of diagonal elements
D.
Difference of diagonal elements
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Solution
The trace of a square matrix is defined as the sum of the elements on its main diagonal.
Correct Answer: C — Sum of diagonal elements
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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
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Solution
A matrix where all elements are zero is called a zero matrix.
Correct Answer: B — Zero matrix
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Q. Which of the following is a square matrix? (2020)
A.
2x3
B.
3x3
C.
4x2
D.
5x1
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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 an identity matrix? (2019)
A.
[[1, 0], [0, 1]]
B.
[[1, 1], [1, 1]]
C.
[[0, 1], [1, 0]]
D.
[[2, 0], [0, 2]]
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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 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]]
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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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