RD Sharma Solutions For Class 12 Maths Exercise 5.5 Chapter 5 Algebra of Matrices

The problems are solved in such a way that they help students understand the topics and improve their problem-solving abilities. Practising lots of examples before solving the main exercise makes them familiar with the formulas and methods. The solutions are prepared by experts at BYJU’S with the aim of helping students score well in the board exams. In the CBSE exam pattern each step carries marks, so the answers are prepared with explanations to make it easy for understanding. RD Sharma Solutions for Class 12 Maths Chapter 5 Algebra of Matrices Exercise 5.5 are provided here.

Download the PDF of RD Sharma Solutions For Class 12 Chapter 5 – Algebra of matrices Exercise 5.5

 

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Access other exercises of RD Sharma Solutions For Class 12 Chapter 5 – Algebra of Matrices

Exercise 5.1 Solutions

Exercise 5.2 Solutions

Exercise 5.3 Solutions

Exercise 5.4 Solutions

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 5 – Algebra of Matrices Exercise 5.5

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 515

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 516

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 517

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 518

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 519

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 520 … (i)

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 521

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 522

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 523 … (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 a skew-symmetric.

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 524

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 525

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 526 … (i)

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 527

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 528

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 529 … (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.

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 530

Solution:

Given,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 531 is a symmetric matrix.

We know that A = [aij]m × n is a symmetric matrix if aij = aji

So,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 532

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 533

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 534

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 535

Hence, x = 4, y = 2, t = -3 and z can have any value.

4. LetRD Sharma Solutions for Class 12 Maths Chapter 5 Image 536. Find matrices X and Y such that X + Y = A, where X is a symmetric and y is a skew-symmetric matrix.

Solution:

Given, 
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 537 Then 
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 538

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 539

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 540

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 541

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 542

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 543

Now,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 544

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 545

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 546

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 547

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 548

Now,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 549

X is a symmetric matrix.

Now,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 550

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 551

-Y T = Y

Y is a skew symmetric matrix.

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 552

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 553

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 554

Hence, X + Y = A


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