# 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

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.

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

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

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.

4. The matrix which follows the condition m>n is called as ____________
a) vertical matrix
b) horizontal matrix
c) diagonal matrix
d) square matrix

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

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.

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=$$\begin{bmatrix}2&2&2\\3&3&3\\4&4&4\end{bmatrix}$$

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

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 = $$\begin{bmatrix}0&0\\0&0\end{bmatrix}$$.

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=$$\begin{bmatrix}2&1&5\\8&1&2\\2&4&8\end{bmatrix}$$

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

Explanation: Minor matrix is not a type of matrix. Scalar, diagonal, symmetric are various type of matrices.

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

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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