29. (i) |2−403| (ii) |acbd|

(i) We know that, Minor of element aij is mij and its co-factor is Aij = (–1)i+j Mij So, M11 = 3 and A11 = (- 1)1 + 1 M11 = 1 * 3 = 3 M12 = 0 and A12 = (-1)1+2 M12 = -1 * 0 = 0 M21 = -4 and A21 = (-1)2+1 M21 = (-1) * (-4) = 4 M22 = 2 and A22 = (-1)2+2 M22 = 1 * 2 = 2 (ii) Given A = |acbd| So, M11 = d and A11 = (-1)1+1 M11 = 1 * d = d M12 = b and A12 = (-1)1+2 M12 = (-1) * b = -b M21 = c and A21 = (-1)2+ 1 M21 = (–1) * c = –c M22 = a and A22 = (-1)2+2 M22 = 1 * a = a

29. (i) $| \begin{matrix} 2 & - 4 \\ 0 & 3 \end{matrix} |$ (ii) $| \begin{matrix} a & c \\ b & d \end{matrix} |$

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Vishal Baghel | Contributor-Level 10

8 months ago

(i) We know that,

Minor of element a_ij is m_ij and its co-factor is A_ij = (–1)^i+j M_ij

So,

M₁₁ = 3 and A₁₁ = (- 1)^{1 + 1} M₁₁ = 1 * 3 = 3

M₁₂ = 0 and A₁₂ = (-1)¹⁺² M₁₂ = -1 * 0 = 0

M₂₁ = -4 and A₂₁ = (-1)²⁺¹ M₂₁ = (-1) * (-4) = 4

M₂₂ = 2 and A₂₂ = (-1)²⁺² M₂₂ = 1 * 2 = 2

(ii) Given A = $| \begin{matrix} a & c \\ b & d \end{matrix} |$

So,

M₁₁ = d and A₁₁

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