Mathematics Questions and Answers – Matrices

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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

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 aij=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=$$\begin{bmatrix}1&2\\1&2\end{bmatrix}$$

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

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

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

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).

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)

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=$$\begin{bmatrix}1\\4\\6\end{bmatrix}$$

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

Explanation: a32 is the element represented in the form aij 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

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 aij follows the condition i=j.
a) 9, 9, 1
b) 2, 9, 7
c) 2, 3, 9
d) 2, 3, 1

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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