**Chapter 4 Determinants and Matrices Ex 4.4**

## Chapter 4 Determinants and Matrices Ex 4.4

**Question 1.**

Solution:

Solution:

**Question 2.Classify the following matrices as a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew- symmetric matrix.**

As every element below the diagonal is zero in matrix A.

∴ A is an upper triangular matrix.

∴ A is a skew-symmetric matrix.

As matrix A has only one row.

∴ A is a row matrix.

As matrix A has all its non-diagonal elements zero and diagonal elements same.

∴ A is a scalar matrix.

As every element above the diagonal is zero in matrix A.

∴ A is a lower triangular matrix.

As matrix A has all its non-diagonal elements zero.

∴ A is a diagonal matrix.

Solution:

In matrix A, all the non-diagonal elements are zero and diagonal elements are one.

∴ A is a unit (identity) matrix.

∴ A is a symmetric matrix.

∴ A is a symmetric matrix.

**Question 3.Which of the following matrices are singular or non-singular?Solution:**

= 3(5 – 8) – 5(-10 – 12) + 7(-4 – 3)

= -9 + 110 – 49 = 52 ≠ 0

∴ A is a non-singular matrix.

**Question 4.Find k, if the following matrices are singular.**

∴ 4(k – 9) – 3(7 – 10) + 1(63 – 10k) = 0

∴ 4k – 36 + 9 + 63 – 10k = 0

∴ -6k + 36 = 0

∴ 6k = 36

∴ k = 6

∴ (k – 1)(4 + 4) – 2(12 – 2) + 3 (-6 – 1) = 0

∴ 8k-8-20-21 =0

∴ 8k = 49

∴ k = 49/8

**Question 5.Solution:**

**Question 6.If A =, find (.Solution:**

**Question 7.Solution:**

**Question 8.Find x, y, z, if is a symmetric matrix.Solution:**

**Question 9.For each of the following matrices, using its transpose, state whether it is symmetric, skew-symmetric or neither.**

ii.

∴ A is neither a symmetric nor skew-symmetric matrix.

iii.

∴ = -A, i.e., A = –

∴ A is a skew-symmetric matrix.

**Question 10.**

∴ = -A, i.e., A = –

∴ A is a skew-symmetric matrix.