Maharashtra State BoardHSC Science (General) 11th
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Answer the following question: Find minor and cofactor of elements of the determinant: |-104-2130-42| - Mathematics and Statistics

Sum

Answer the following question:

Find minor and cofactor of elements of the determinant:

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

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

M11 = `|(1, 3),(-4, 2)|` = 2 + 12 = 14

∴ C11 = (– 1)1+1 M11 = 1(14) = 14

M12 = `|(-2, 3),(0, 2)|` = – 4 – 0 = –  4

∴ C12 = (– 1)1+2 M12 = (– 1)(– 4) = 4

M13 = `|(-2, 1),(0, -4)|` = 8 –  0 = 8

∴ C13 = (– 1)1+3 M13 = 1(8) = 8

M21 = `|(0, 4),(-4, 2)|` = 0 + 16 =16

∴ C21 = (–1)2+1 M21 = (–1)(16) = – 16

M22 = `|(-1, 4),(0, 2)|` = –2 – 0 = – 2

∴ C22 = (–1)2+2 M22 = 1(–2) = –2

M23 = `|(-1, 0),(0, -4)|` = 4 – 0 =  4

∴ C23 = (–1)2+3 M23 = (–1)(4) = –4

M31 = `|(0, 4),(1, 3)|` = 0 – 4 = – 4

∴ C31 = (–1)3+1 M31 = 1(–4) = –4

M32 = `|(-1, 4),(-2, 3)|` = –3 + 8 = 5

∴ C32 = (–1)3+2 M32 = (–1)(5) = –5

M33 = `|(-1, 0),(-2, 1)|` = –1 + 0 = –1

∴ C33 = (–1)3+3 M33 = 1(–1) = –1

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
Miscellaneous Exercise 4(A) | Q II. (4) (i) | Page 76
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