Mathematics Questions and Answers – Types of Matrices

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

1. The matrix which follows the conditions m=n is called?
a) Square matrix
b) Rectangular matrix
c) Scalar matrix
d) Diagonal matrix
View Answer

Answer: a
Explanation: A square matrix is a matrix in which the number of rows(m) is equal to the number of columns(n). Therefore, the matrix which follows the condition m=n is a square matrix.
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2. Consider the matrix A=\(\begin{bmatrix}4&6&9\\12&11&10\end{bmatrix}\). What is the type of matrix?
a) Row matrix
b) Column matrix
c) Horizontal matrix
d) Vertical matrix
View Answer

Answer: c
Explanation: The matrix in which number of rows is smaller than the number of columns is called is called a horizontal matrix. In the given matrix A=\(\begin{bmatrix}4&6&9\\12&11&10\end{bmatrix}\), m=3 and n=2 i.e.
3<2. Hence, it is a horizontal matrix.

3. The matrix A=\(\begin{bmatrix}4\\12\\36\end{bmatrix}\) is _____________
a) row matrix
b) scalar matrix
c) horizontal matrix
d) column matrix
View Answer

Answer: d
Explanation: The given matrix A = \(\begin{bmatrix}4\\12\\36\end{bmatrix}\) is of the order 3×1. The matrix has only one column (n=1). Hence, it is a column matrix.
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4. The matrix which follows the condition m>n is called as ____________
a) vertical matrix
b) horizontal matrix
c) diagonal matrix
d) square matrix
View Answer

Answer: a
Explanation: The matrix in which the number of columns is greater than the number of rows is called a vertical matrix. There the matrix which follows the condition m>n is a vertical matrix.

5. Find the value of a,b,c,d if \(\begin{bmatrix}a+b&c\\a-b&2c+d\end{bmatrix}\)=\(\begin{bmatrix}3&2\\1&6\end{bmatrix}\).
a) 3, 2, 1, 4
b) 3, 2, 1, 6
c) 2, 2, 2, 2
d) 2, 1, 2, 2
View Answer

Answer: d
Explanation: The two matrices \(\begin{bmatrix}a+b&c\\a-b&2c+d\end{bmatrix}\)and\(\begin{bmatrix}3&2\\1&6\end{bmatrix}\) are equal matrices. Comparing the two matrices, we get
a-b=3, c=2, a-b=1, 2c+d=6
Solving the above equations, we get a=2, b=1, c=2, d=2.
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6. Which of the following is a diagonal matrix.
a) A=\(\begin{bmatrix}0&2&1\\2&0&1\\2&1&0\end{bmatrix}\)
b) A=\(\begin{bmatrix}5&1&0\\0&5&0\\0&0&5\end{bmatrix}\)
c) A=\(\begin{bmatrix}4&0&0\\0&5&0\\0&0&9\end{bmatrix}\)
d) A=\(\begin{bmatrix}2&2&2\\3&3&3\\4&4&4\end{bmatrix}\)
View Answer

Answer: c
Explanation: The matrix is said to be a diagonal matrix if the elements along the diagonal of the matrix are non – zero.
i.e. aij=0 for i≠j and aij≠0 for i=j.
Therefore, the matrix A=\(\begin{bmatrix}4&0&0\\0&5&0\\0&0&9\end{bmatrix}\) is a diagonal matrix.

7. State whether the given statement is true or false.
The matrix A = \(\begin{bmatrix}0&0\\0&0\end{bmatrix}\)
a) True
b) False
View Answer

Answer: a
Explanation: The given statement is true. A matrix is called a null or zero matrix if the value of all the elements in the matrix is 0. Thus A = \(\begin{bmatrix}0&0\\0&0\end{bmatrix}\).
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8. Which of the following is a scalar matrix?
a) A=\(\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}\)
b) A=\(\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}\)
c) A=\(\begin{bmatrix}7&0&0\\0&2&0\\0&0&5\end{bmatrix}\)
d) A=\(\begin{bmatrix}2&1&5\\8&1&2\\2&4&8\end{bmatrix}\)
View Answer

Answer: a
Explanation: A matrix is called a scalar matrix if the elements along the diagonal of the matrix are equal and are non-zero i.e. aij=k for i=j and aij=0 for i≠j.
Therefore, the matrix A=\(\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}\) is a scalar matrix.

9. Which of the following is not a type of matrix?
a) Scalar matrix
b) Diagonal matrix
c) Symmetric matrix
d) Minor matrix
View Answer

Answer: d
Explanation: Minor matrix is not a type of matrix. Scalar, diagonal, symmetric are various type of matrices.
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10. Find a,b,c,d if \(\begin{bmatrix}a&b+c\\c+d&b\end{bmatrix}\)=\(\begin{bmatrix}3&2\\3&-1\end{bmatrix}\) are equal matrices.
a) 3, 0, 1, -1
b) 1,-3, 0, 3
c) 3, -1, 3, 0
d) 3, 3, -1, -1
View Answer

Answer: c
Explanation: The two matrices \(\begin{bmatrix}a&b+c\\c+d&b\end{bmatrix}\)and\(\begin{bmatrix}3&2\\3&-1\end{bmatrix}\) are equal matrices. Comparing the two matrices, we get
a=3, b+c=2, c+d=3, b=-1
Solving the above equations, we get a=3, b=-1, c=3, d=0.

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

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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