Question

निम्नलिखित सारणिक के अवयव के उपसारणिक एवं सहखंड लिखिए।

`|(1,0,4),(3,5,-1),(0,1,2)|`

Answer 1

`|(1,0,4),(3,5,-1),(0,1,2)|`

उपसारणिक:

M₁₁ = `|(5,-1),(1,2)|`

= 5 × 2 − (−1) × 1

= 10 + 1

= 11

M₁₂ = `|(3,-1),(0,2)|`

= 3 × 2 − (−1) × 0

= 6 + 0

= 6

M₁₃ = `|(3,5),(0,1)|`

= 3 × 1 − 5 × 0

= 3 − 0

= 3

M₂₁ = `|(0,4),(1,2)|`

= 0 × 2 − 1 × 4

= 0 − 4

= −4

M₂₂ = `|(1,4),(0,2)|`

= 1 × 2 − 4 × 0

= 2 − 0

= 2

M₂₃ = `|(1,0),(0,1)|`

= 1 × 1 − 0 × 0

= 1 − 0

= 1

M₃₁ = `|(0,4), (5, -1)|`

= (−1) × 0 − 4 × 5

= 0 − 20

= −20

M₃₂ = `|(1,4),(3,-1)|`

= 1 × (−1) − 3 × 4

= (−1) − 12

= −13

M₃₃ = `|(1,0),(3,5)|`

= 1 × 5 − 0 × 3

= 5 − 0

= 5

सहखंड:

A₁₁ = (−1)¹⁺¹ M₁₁

= 11 × 1

= 11

A₁₂ = (−1)¹⁺² M₁₂

= (−1) × 6

= −6

A₁₃ = (−1)¹⁺³ M₁₃

= 1 × 3

= 3

A₂₁ = (−1)²⁺¹ M₂₁

= (−1) × (−4)

= 4

A₂₂ = (−1)²⁺² M₂₂

= 1 × 2

= 2

A₂₃ = (−1)²⁺³ M₂₃

= (−1) × 1

= −1

A₃₁ = (−1)³⁺¹ M₃₁

= 1 × (−20)

= −20

A₃₂ = (−1)³⁺² M₃₂

= (−1) × (−13)

= −13

A₃₃ = (−1)³⁺³ M₃₃

= 1 × 5

= 5