RD Sharma Solutions For Class 12 Maths Exercise 5.4 Chapter 5 Algebra of Matrices

In order to excel in the CBSE exam for Class 12, students can use the solutions of Exercise 5.4 available on the website. By practising regularly the students can obtain worthy results in the Class 12 exams by using the RD Sharma Solutions. The PDF of solutions of exercise 5.4 primarily helps students from the exam point of view. This exercise mainly contains solved problems based on the concept of symmetric and skew-symmetric matrices. RD Sharma Solutions for Class 12 Maths Chapter 5 Algebra of Matrices Exercise 5.4 are provided here.

Download the PDF of RD Sharma Solutions For Class 12 Chapter 5 – Algebra of matrices Exercise 5.4

 

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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 5.5 Solutions

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 5 – Algebra of Matrices Exercise 5.4

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 448

(i) (2A)T = 2 AT

(ii) (A + B)T = AT + BT

(iii) (A – B)T = AT – BT

(iv) (AB)T = BT AT

Solution:

(i) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 449

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 450

Put the value of A

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 451

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 452

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 453

L.H.S = R.H.S

(ii) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 454

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 455

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 456

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 457

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 458

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 459

L.H.S = R.H.S

Hence proved.

(iii) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 460

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 461

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 462

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 463

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 464

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 465

L.H.S = R.H.S

(iv) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 466

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 467

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 468

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 469

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 470

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 471

So,

 
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 472

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 473

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 474

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 475

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 476

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 477

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 478

L.H.S = R.H.S

So, 
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 479

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 480

(i) A + B)T = AT + BT

(ii) (AB)T = BT AT

(iii) (2A)T = 2 AT

Solution:

(i) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 481

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 482

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 483

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 484

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 485

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 486

L.H.S = R.H.S

So, 
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 487

(ii) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 488

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 489

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 490

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 491

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 492

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 493

L.H.S = R.H.S

So, 
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 494

(iii) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 495

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 496

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 497

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 498

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 499

L.H.S = R.H.S

So,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 500

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 501

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 502

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 503

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 504

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 505

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 506

L.H.S = R.H.S

So,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 507

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 508

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 509

Now we have to find (AB)T

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 510

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 511

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 512

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 513

So,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 514


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