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Find the value of determinant expanding along third column |-112-23-4-340| - Mathematics and Statistics

Sum

Find the value of determinant expanding along third column

`|(-1, 1, 2),(-2, 3, -4),(-3, 4, 0)|`

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Solution

Here, `|("a"_11, "a"_12, "a"_13),("a"_21, "a"_22, "a"_23),("a"_31, "a"_32, "a"_33)| = |(-1, 1, 2),(-2, 3, -4),(-3, 4, 0)|`

Expansion along the third column

= a13 C13 + a23 C23 + a33 C33

= `2 xx (-1)^(1 + 3) |(-2, 3),(-3, 4)| -4 xx (-1)^(2 + 3)|(-1, 1),(-3, 4)| + 0 xx (-1)^(3 + 3)|(-1, 1),(-2, 3)|`

= 2 (– 8 + 9) + 4 (– 4 + 3) + 0

= 2 – 4

= – 2

Concept: Minors and Cofactors of Elements of Determinants
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Determinants and Matrices
Exercise 4.1 | Q 6 | Page 64
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