Question

1. Which of the following statement is not true?
(a) All identity matrices are square matrix
(b) All null matrices are square matrix
(c) For a square matrix number of rows is equal to the number of columns
(d) A square matrix all of whose elements except those in the leading diagonal are zero is the diagonal matrix

Answer 1

Answer:

b) All null matrices are square matrix

Step-by-step explanation:

It is not always that null matrices are square matrix.

example : [0 0]

Here, the order of matrix is 1 × 2 i.e.,

no. of rows = 1

no. of columns = 2

Let me aware you, that a SQUARE MATRIX is a matrix in which the number of rows equals the number of columns.

So, with the above statement,

no. of rows - 1 ≠ no. of columns - 2

Hence, it is clear that null matrices are not always square matrices.

Answer 2

Given :  Statements about square matrix

To Find : Which of the following statement is not true?

(a) All identity matrices are square matrix

(b) All null matrices are square matrix

(c) For a square matrix number of rows is equal to the number of columns

(d) A square matrix all of whose elements except those in the leading diagonal are zero is the diagonal matrix

Solution:

identity matrices  are  n × n square matrices with 1 on diagonal elements and all other elements zero

Hence All identity matrices are square matrix   - TRUE

(b) All null matrices are square matrix  - FALSE

Null Matrices are matrices of m * n order n which all elements are zero

they are square matrix if m = n other wise they are not square matric

Hence

All null matrices are square matrix is NOT TRUE

(c) For a square matrix number of rows is equal to the number of columns

YES Hence TRUE

(d) A square matrix all of whose elements except those in the leading diagonal are zero is the diagonal matrix  TRUE

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