Tamil Nadu Board of Secondary EducationHSC Arts Class 11

Construct an m × n matrix A = [aij], where aij is given by aij = ij(i-2j)22 with m = 2, n = 3 - Mathematics

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Sum

Construct an m × n matrix A = [aij], where aij is given by

aij = `("i" - 2"j")^2/2` with m = 2, n = 3

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Solution

To construct 2 × 3 matrices.

A = `["a"_"ij"]_(2 xx 3) = [("a"_11, "a"_12, "a"_13),("a"_2, "a"_22, "a"_23)]`

a11 = `(1 - 2 xx 1)^2/2`

= `(1 - 2)^2/2` 

= `(- 1)^2/2`

= `1/2`

a12 = `(1 - 2 xx 2)^2/2`

= `(1 - 4)^2/2` 

= `(- 3)^2/2`

= `9/2`

a13 = `(1 - 2 xx 3)^2/2`

= `(1 - 6)^2/2` 

= `(- 5)^2/2`

= `25/2`

a21 = `(2 - 2 xx 1)^2/2`

= `(2 - 2)^2/2` 

= `0/2`

= 0

a22 = `(2 - 2 xx 2)^2/2`

= `(2 - 4)^2/2` 

= `(- 2)^2/2`

= `4/2`

= 2

a23 = `(2 - 2 xx 3)^2/2`

= `(2 - 6)^2/2` 

= `(- 4)^2/2`

= `16/2`

= 8

∴ The required 2 × 3 martix is A = `[(1/2, 9/2, 25/2),(0, 2, 8)]`

Concept: Matrices
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Chapter 7: Matrices and Determinants - Exercise 7.1 [Page 17]

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Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 7 Matrices and Determinants
Exercise 7.1 | Q 1. (i) | Page 17

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