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RD Sharma - Volume 1

5. Algebra of Matrices

Exercise 5.1

1 2 A 2 B 3 4 A 4 B 4 C 4 D 5 A 5 B 5 C 5 D 5 E 5 F 5 G 6 A 6 B 6 C 6 D 6 E 7 A 7 B 7 C 8 9 10 11 12 13 14 15 16 17 A 17 B 17 C 18 19 20 21

Exercise 5.2

1 A 1 B 2 A 3 4 5 6 7 8 9 10 11 12 13 14 15 A 15 B 15 C 16 17 18 A 18 B 19 A 19 B 20 21 22

Exercise 5.3

1 A 1 B 1 C 2 A 2 B 2 C 3 A 3 B 3 C 3 D 4 A 4 B 5 A 5 B 5 C 6 7 8 9 10 11 12 13 14 15 16 A 16 B 17 A 17 B 18 19 20 21 22 23 24 A 24 B 25 26 27 28 29 30 31 22 33 34 35 36 37 38 39 40 A 40 B 40 C 40 D 41 42 43 44 45 46 47 48 A 48 B 48 C 48 D 48 E 48 F 49 50 51 52 53 54 A 54 B 55 56 57 58 59 60 61 62 63 64 65 A 65 B 65 C 65 D 66 67 68 69 70 71 72 73 74 75 76 77 78 79

Exercise 5.4

1 A 1 B 1 C 1 D 2 3 A 3 B 3 C 4 5 6 A 6 B 7 8 9 10

Exercise 5.5

1 2 3 4 5 6 7 8

Very short answer

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MCQ

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Q. 203.7( 3 Votes )

For any square ma

Class 12th RD Sharma - Volume 1 5. Algebra of Matrices

Answer :

Here, we have any square matrix

To Find: AA^T is symmetric or skew – symmetric

Proof: Firstly, we take the transpose of AA^T, so we get

(AA^T)^T = (A^T)^T A^T [∵ (AB)^T = B^TA^T]

⇒ (AA^T)^T = AA^T [∵ (A^T)^T = A]

∴ AA^T is a symmetric matrix

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