# Simultaneous Algebraic Equations Questions and Answers – Introduction to Matrices

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This set of Numerical Methods Multiple Choice Questions & Answers (MCQs) focuses on “Introduction to Matrices”.

1. Which of the following option is correct when addition of two matrices A and B is possible?
a) both are rectangular
b) both have same order
c) no of columns of A is equal to columns of B
d) no of rows of A is equal to no of columns of B

Explanation: This is because addition is only possible if each element in one matrix has a corresponding element in the second matrix. This will occur when both the matrices have same order.

2. If A is a symmetric matrix, then At will be equal to which of the following?
a) A
b) |A|
c) 0
d) diagonal matrix

Explanation: This is because for a symmetric matrix, elements in the row of a certain column are same as the elements in a certain row. Hence, a matrix and its transpose remain same.

3. Which of the following option is correct when multiplication of two matrices A and B is possible?
a) both are rectangular
b) both have same order
c) number of rows of A is equal to rows of B
d) number of rows of A is equal to number of columns of B

Explanation: Multiplication is possible only when number of columns of A is equal to rows of B. And, the matrices having same order do follow this property.

4.The matrix $$\begin{bmatrix}5&0\\0&5\end{bmatrix}$$ is?
a) Even matrix
b) Odd matrix
c) Scalar matrix
d) Identity matrix

Explanation: If the identity matrix has other numbers in place of 1 it is said to be a scalar matrix. Identity matrix is also a type of scalar matrix.

5. What do we call the number of non-zero rows in an echelon matrix?
a) reduced echelon matrix
b) order of a matrix
c) determinant of a matrix
d) rank of a matrix

Explanation: The number of non-zero rows in an echelon matrix is called as rank of a matrix. This is a method used to determine the rank of a matrix.

6. If AB exists, then (AB)-1 will be equal to which of the following?
a) A-1 B-1
b) B-1 A-1
c) AB
d) BA

Explanation: Inverse acts on product inversely. The inverse operation acting on the product first applies on the last matrix and then moves towards the first matrix if product is of more than two matrices.

7. Which of the following is true if two matrices A and B are equal?
a) both are rectangular
b) both have same order
c) number of columns of A is equal to columns of B
d) both have same order and equal corresponding elements

Explanation: Both should have same order and equal corresponding elements. This is the criterion for being equal.

8. What do we call the matrices obtained by changing rows and columns?
a) rectangular matrix
b) transpose
c) symmetric
d) scalar

Explanation: Matrix obtained by changing rows and columns is called as transpose. It can be obtained by exchanging the indices of elements of the matrix.

9. What is the order of the matrix with m rows and n columns?
a) m + n
b) n x n
c) m x m
d) m x n

Explanation: The order of a matrix is given by number of rows X number of columns. So, here it is m X n.

10. What is the order of the matrix [2 4 3]?
a) 1 X 3
b) 3 X 1
c) 1 X 1
d) 3 X 3

Explanation: Order of a matrix is given by number of rows X no. of columns. Here, number of rows is 1 and number of columns is 3.

11. Which of the following is true if A is a singular matrix?
a) It contains all elements equal to 1
b) It contains single element
c) Its determinant is zero
d) It contains all elements equal to 0

Explanation: A matrix is called singular if its determinant is equal to zero. A matrix containing all elements equal to 0 is called as a null matrix.

12. What is x, if P = $$\begin{bmatrix}1&4\\2&x\end{bmatrix}$$ is a singular matrix?
a) 5
b) 6
c) 7
d) 8