Matrices Questions and Answers

This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Matrices”.

1. If the order of the matrix is m×n, then how many elements will there be in the matrix?
a) mn
b) m² n²
c) mn²
d) 2mn
View Answer

Answer: a
Explanation: The number of elements for a matrix with the order m×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.

2. Which of the following is a matrix of the order 2×2 where the equation of the elements is given by a_ij=i+j.
a) A=\(\begin{bmatrix}1&1\\1&1\end{bmatrix}\)
b) A=\(\begin{bmatrix}4&5\\4&1\end{bmatrix}\)
c) A=\(\begin{bmatrix}2&3\\3&4\end{bmatrix}\)
d) A=\(\begin{bmatrix}1&2\\1&2\end{bmatrix}\)
View Answer

Answer: c
Explanation: a₁₁=1+1=2, a₁₂=1+2=3, a₂₁=2+1=3, a₂₂=2+2=4
∴ A=\(\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22} \end{bmatrix}=\begin{bmatrix}2&3\\3&4\end{bmatrix}\).

3. What is the order of the matrix A=\(\begin{bmatrix}3&5\\7&9\end{bmatrix}\)?
a) 2×3
b) 2×2
c) 3×3
d) 4×4
View Answer

Answer: b
Explanation: The number of rows (m) and the number of columns (n) in the given matrix A=\(\begin{bmatrix}3&5\\7&9\end{bmatrix}\) is 2. Therefore, the order of the matrix is 2×2(m×n).

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4. The order of the matrix A=\(\begin{bmatrix}1&5&9\\4&8&6\end{bmatrix}\) is 2×3.
a) True
b) False
View Answer

Answer: b
Explanation: The given statement is false. In the matrix A=\(\begin{bmatrix}1&5&9\\4&8&6\end{bmatrix}\) the number of rows(m) is 3 and the number of columns(n) is 2. Therefore, the order of the matrix is 3×2.

5. In a matrix with 9 elements, then the possible ordered pairs are (3, 3), (1, 9), (9, 1).
a) True
b) False
View Answer

Answer: a
Explanation: The given statement is true. The possible orders in which the matrix can be formed are 3×3,9×1,1×9. Therefore, the ordered pairs are (3,3),(1,9),(9,1).

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6. Which of the following is not a possible ordered pair for a matrix with 6 elements.
a) (2,3)
b) (3,2)
c) (1,6)
d) (3,1)
View Answer

Answer: d
Explanation: The possible orders in which the matrix with 6 elements can be formed are 2×3, 3×2, 1×6, 6×1. Therefore, the possible orders pairs are (2,3), (3,2), (1,6), (6,1). Thus, (3,1) is not possible.

7. Which of the following matrix is of the order 3×4.
a) A=\(\begin{bmatrix}3&4\\3&5\\4&5\end{bmatrix}\)
b) A=\(\begin{bmatrix}1&2&3\\5&7&9\end{bmatrix}\)
c) A=\(\begin{bmatrix}4&5&6 \\5&2&6\\6&4&7\\7&7&1\end{bmatrix}\)
d) A=\(\begin{bmatrix}1\\4\\6\end{bmatrix}\)
View Answer

Answer: c
Explanation: The matrix A=\(\begin{bmatrix}4&5&6\\5&2&6\\6&4&7\\7&7&1\end{bmatrix}\) is a 3×4 matrix as it as 3 rows and 4 columns.

8. Consider the matrix A=\(\begin{bmatrix}2&4&5\\1&6&4\\2&8&9\end{bmatrix}\). Find the element a₃₂.
a) 5
b) 6
c) 4
d) 8
View Answer

Answer: d
Explanation: a₃₂ is the element represented in the form a_ij i is the row number and j is the column number. Therefore, the element a₃₂ is the element in the third row (i=3)and second column (j=2) which is 8.

9. What is the order of the matrix A=\(\begin{bmatrix}2&3\\1&9\\5&2\end{bmatrix}\)?
a) 2×3
b) 3×2
c) 2×2
d) 3×3
View Answer

Answer: b
Explanation: The given matrix A=\(\begin{bmatrix}2&3\\1&9\\5&2\end{bmatrix}\) has 3 rows and 2 columns. Therefore, the order of the matrix is 3×2.

10. Given a matrix A=\(\begin{bmatrix}2&3&9\\3&9&6\\1&6&7\end{bmatrix}\), which of the elements a_ij follows the condition i=j.
a) 9, 9, 1
b) 2, 9, 7
c) 2, 3, 9
d) 2, 3, 1
View Answer

Answer: b
Explanation: The elements following the condition i=j will have the same row number and column number. The elements are a₁₁, a₂₂, a₃₃ which in the matrix A are 2, 3, 9 respectively.

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