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Construct a matrix A = = [aij]3×2 whose element aij is given by aij = (i+j)35 - Mathematics and Statistics

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प्रश्न

Construct a matrix A = [aij]3 × 2 whose element aij is given by

aij = `(("i" + "j")^3)/5`

योग
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उत्तर

A = [aij]3 × 2 = `[("a"_11, "a"_12),("a"_21, "a"_22),("a"_31, "a"_32)]`

Given that aij = `(("i" + "j")^3)/5`

∴ a11 = `((1 + 1)^3)/5 = 2^3/5 = 8/5`

a12 = `((1 + 2)^3)/5 = 3^3/5 = 27/5`

a21 = `((2 + 1)^3)/5 = 3^3/5 = 27/5`

a22 = `((2 + 2)^3)/5 = 4^3/5 = 64/5`

a31 = `((3 + 1)^3)/5 = 4^3/5 = 64/5`

a32 = `((3 + 2)^3)/5 = 5^3/5 = 125/5`

∴ A = `[(8/5, 27/5),(27/5, 64/5),(64/5, 125/5)] = 1/5[(8, 27),(27,64),(64, 125)]`

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अध्याय 4: Determinants and Matrices - Exercise 4.4 [पृष्ठ ८२]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board
अध्याय 4 Determinants and Matrices
Exercise 4.4 | Q 1. (iii) | पृष्ठ ८२

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