Evaluate: a + ibc + id-c + ida - ib
Find the co-factor of a12 in the following:
2-3560415-7
Using properties of determinants, prove the following:
αβγα2β2γ2β + γ γ + α α + β = α - β β - γ γ - α α + β + γ
∆ = α β γα2 β2 γ2β + γ γ + α α + βApplying R3→ R3 + R1∆ = α β γα2 β2 γ2α+ β + γ α+ β + γ α+ β + γ = α+ β + γ α β γα2 β2 γ21 1 1Applying C1→C1 - C2 and C2→C2 - C3
∆ = α + β + γ = α - β β - γ γα2 - β2 β2 - γ 2 γ20 0 0 = (α + β + γ ) (α - β) (β - γ ) 1 1 1α + β β + γ γ0 0 0 = (α + β + γ ) (α - β) (β - γ ) 1 (β + γ ) -1 (α + β) = (α - β) (β - γ ) (α + β + γ ) ( β + γ - α - β ) = (α - β) (β - γ ) (γ - α ) (α + β + γ )
Hence proved.
Write the value of the determinant 2 3 4 5 6 86x 9x 12x
Using properties of determinants prove the following:
a bca - b b - c c - ab + c c + a a + b = a3 + b3 + c3 - 3abc
Find the minor of the element of second row and third column ( a23 ) in the following determinant:
2 -3 56 0 41 5 -7
Using properties of determinants show the following:
b + c 2 ab caab a + c 2 bcac bc a + b 2 = 2abc ( a + b + c )3
Using properties of determinants, prove that
- a2 ab ac ba -b2 bc ca cb - c2 = 4 a2b2c2
Using matrix method, solve the following system of equations:
2x + 3y + 10z = 4, 4x - 6y + 5z, 6x + 9y - 20z; x, y, z ≠ 0
If ∆ = 5 3 8 2 0 1 1 2 3 , white the cofactor of the element a32.
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