RD Sharma Solutions For Class 12 Maths Exercise 5.2 Chapter 5 Algebra of Matrices

RD Sharma Class 12 Solutions Chapter 5 Ex 5.2 PDF Free Download

Regular practice on a daily basis is the main thing that should be done by the students in the Mathematics field. Highly experienced subject experts having a vast knowledge of concepts prepare the answers, which match the understanding ability of the students. RD Sharma Solutions for Class 12 can be used by students in order to excel in the subject by obtaining a good academic score. This exercise covers the topic addition of matrices with explanatory answers. RD Sharma Solutions for Class 12 Maths Chapter 5 Algebra of Matrices Exercise 5.2 are provided here.

Download the PDF of RD Sharma Solutions For Class 12 Chapter 5 – Algebra of matrices Exercise 5.2

 

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

Exercise 5.1 Solutions

Exercise 5.3 Solutions

Exercise 5.4 Solutions

Exercise 5.5 Solutions

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 5 – Algebra of Matrices Exercise 5.2

1. Compute the following sums:

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 134

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 135

Solution:

(i) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 136

Corresponding elements of two matrices should be added

Therefore, we get

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 137

Therefore,
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 138

(ii) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 139

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 140

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 141

Therefore,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 142

RD Sharma Solutions for Class 12 Maths Chapter 5 Image143

Find each of the following:

(i) 2A – 3B

(ii) B – 4C

(iii) 3A – C

(iv) 3A – 2B + 3C

Solution:

(i) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 144

First we have to compute 2A

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 145

Now by computing 3B we get,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 146

Now by we have to compute 2A – 3B we get

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 147

Therefore

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 148

(ii) Given
RD Sharma Solutions for Class 12 Maths Chapter 5 Image 149

First we have to compute 4C,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 150

Now,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 151

Therefore we get,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 152

(iii) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 153

First we have to compute 3A,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 154

Now,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 155

Therefore,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 156

(iv) Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 157

First we have to compute 3A

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 158

Now we have to compute 2B

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 159

By computing 3C we get,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 160

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 161

Therefore,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 162

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 163

(i) A + B and B + C

(ii) 2B + 3A and 3C – 4B

Solution:

(i) Consider A + B,

A + B is not possible because matrix A is an order of 2 x 2 and Matrix B is an order of 2 x 3, so the Sum of the matrix is only possible when their order is same.

Now consider B + C

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 164

(ii) Consider 2B + 3A

2B + 3A also does not exist because the order of matrix B and matrix A is different, so we cannot find the sum of these matrix.

Now consider 3C – 4B,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 165

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 166

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 167

Now we have to compute 2A – 3B + 4C

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 168

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 169

5. If A = diag (2 -5 9), B = diag (1 1 -4) and C = diag (-6 3 4), find

(i) A – 2B

(ii) B + C – 2A

(iii) 2A + 3B – 5C

Solution:

(i) Given A = diag (2 -5 9), B = diag (1 1 -4) and C = diag (-6 3 4)

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 170

(ii) Given A = diag (2 -5 9), B = diag (1 1 -4) and C = diag (-6 3 4)

We have to find B + C – 2A

Here,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 171

Now we have to compute B + C – 2A

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 172

(iii) Given A = diag (2 -5 9), B = diag (1 1 -4) and C = diag (-6 3 4)

Now we have to find 2A + 3B – 5C

Here,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 173

Now consider 2A + 3B – 5C

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 174

6. Given the matrices

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 175

Verify that (A + B) + C = A + (B + C)

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 176

Now we have to verify (A + B) + C = A + (B + C)

First consider LHS, (A + B) + C,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image177

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 178

Now consider RHS, that is A + (B + C)

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 179

Therefore LHS = RHS

Hence (A + B) + C = A + (B + C)

7. Find the matrices X and Y,

C:\Users\tnluser\Downloads\CodeCogsEqn (51).gif

Solution:

Consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 181

Now by simplifying we get,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 182

Therefore,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 183

Again consider,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 184

Now by simplifying we get,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 185

Therefore,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 186

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 187

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 188

Now by transposing, we get

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 189

Therefore,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 190

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 191

Solution:

Given

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 192

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 193

Now by multiplying equation (1) and (2) we get,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 194

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 195

Now by adding equation (2) and (3) we get,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 196

Now by substituting X in equation (2) we get,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 197

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 198

Solution:

Consider

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 199

Now, again consider

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 200

Therefore,

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 201

And

RD Sharma Solutions for Class 12 Maths Chapter 5 Image 202


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