RD Sharma Solutions for Class 12 Maths Exercise 5.5 Chapter 5 Algebra of Matrices are provided here. The problems are solved in such a way that they help students understand the topics and improve their problem-solving abilities. Practising examples before solving the main exercise makes them familiar with the formulae and methods.
The RD Sharma Solutions are prepared by subject experts at BYJU’S with the aim of helping students score well in the board exam. In the CBSE exam pattern, each step carries marks, so the answers are prepared with explanations to make them easy to understand. RD Sharma Solutions for Class 12 Maths Chapter 5 Algebra of Matrices Exercise 5.5 are provided here.
RD Sharma Solutions for Class 12 Chapter 5 – Algebra of Matrices Exercise 5.5
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Solution:
Given
Consider,
… (i)
… (ii)
From (i) and (ii), we can see that
A skew-symmetric matrix is a square matrix whose transpose equal to its negative, that is,
X = – XT
So, A – AT is skew-symmetric.
Solution:
Given
Consider,
… (i)
… (ii)
From (i) and (ii), we can see that
A skew-symmetric matrix is a square matrix whose transpose equals its negative, that is,
X = – XT
So, A – AT is a skew-symmetric matrix.
Solution:
Given,
is a symmetric matrix.
We know that A = [aij]m × n is a symmetric matrix if aij = aji
So,
Hence, x = 4, y = 2, t = -3 and z can have any value.
4. Let
. Find matrices X and Y such that X + Y = A, where X is a symmetric and y is a skew-symmetric matrix.
Solution:
Given,
Then
Now,
Now,
X is a symmetric matrix.
Now,
-Y T = Y
Y is a skew-symmetric matrix.
Hence, X + Y = A
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