Tamil Nadu Board of Secondary EducationHSC Science Class 11th

# Construct an m × n matrix A = [aij], where aij is given byaij = ij|3i-4j|4 with m = 3, n = 4 - Mathematics

Sum

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

aij = |3"i" - 4"j"|/4 with m = 3, n = 4

#### Solution

To construct a 3 × 4 matrices.

A = ["a"_"ij"]_(5 xx 4) = [("a"_11, "a"_12, "a"_13, "a"_14),("a"_21, "a"_22, "a"_24, "a"_24),("a"_31, "a"_32, "a"_33, "a"_34)]

a11 = |3 xx 1 - 4 xx 1|/4

= |3 - 4|/4

= |- 1|/4

= 1/4

a12 = |3 xx 1 - 4 xx 2|/4

= |3 - 8|/4

= |- 5|/4

= 5/4

a13 = |3 xx 1 - 4 xx 3|/4

= |3 - 12|/4

= |- 9|/4

= 9/4

a14 = |3 xx 1 - 4 xx 4|/4

= |3 - 16|/4

= |- 13|/4

= 13/4

a21 = |3 xx 2 - 4 xx 1|/4

= |6 - 4|/4

= |2|/4

= 2/4

= 1/2

a22 = |3 xx 2 - 4 xx 2|/4

= |6 - 8|/4

= |- 2|/4

= 2/4

= 1/2

a23 = |3 xx 2 - 4 xx 3|/4

= |6 - 12|/4

= |- 6|/4

= 6/4

= 3/2

a24 = |3 xx 2 - 4 xx 4|/4

= |6 - 16|/4

= |- 10|/4

= 10/4

= 5/2

a31 = |3 xx 3 - 4 xx 1|/4

= |9 - 4|/4

= |5|/4

= 5/4

a32 = |3 xx 3 - 4 xx 2|/4

= |9 - 8|/4

= |1|/4

= 1/4

a33 = |3 xx 3 - 4 xx 3|/4

= |9 - 12|/4

= |- 3|/4

= 3/4

a34 = |3 xx 3 - 4 xx 4|/4

= |9 - 16|/4

= |- 7|/4

= 7/4

∴ The required 3 × 4 matrix is

A = [(1/4, 5/4, 9/4, 13/4),(1/2, 1/2, 3/2, 5/2),(5/4, 1/4, 3/4, 7/4)]

Concept: Matrices
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#### APPEARS IN

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