Question

Answer the following question:

Find minor and cofactor of elements of the determinant:

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

Answer 1

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