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
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.
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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=\(\begin{bmatrix}1&2\\1&2\end{bmatrix}\)
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.
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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 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
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.
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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
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.

Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter