Advertisements
Advertisements
Question
Evaluate the following determinants: `|(1, "i", 3),("i"^3, 2, 5),(3, 2, "i"^4)|`
Solution
`|(1, "i", 3),("i"^3, 2, 5),(3, 2, "i"^4)|`
= `|(1, "i", 3),(-"i", 2, 5),(3, 2, 1)|` ...[∵ i2 = – 1, i4 = 1]
= `1|(2, 5),(2, 1)| - "i"|(-"i", 5),(3, 1)| + 3|(-"i", 2),(3, 2)|`
= 1(2 – 10) – i(– i –15) + 3(– 2i – 6)
= – 8 + i2 + 15i – 6i – 18
= i2 – 26 + 9i
= – 1 – 26 + 9i ...[∵ i2 = – 1]
= – 27 + 9i
APPEARS IN
RELATED QUESTIONS
Evaluate the following determinant:
`|(4, 7),(-7, 0)|`
Find the value(s) of x, if `|(2, 3),(4, 5)| = |(x, 3),(2x, 5)|`
Without expanding evaluate the following determinant:
`|(2, 7, 65),(3, 8, 75),(5, 9, 86)|`
Evaluate: `|(2, -5, 7),(5, 2, 1),(9, 0, 2)|`
Find the minors and cofactors of all the elements of the following determinant.
`|(1,-3,2),(4,-1,2),(3,5,2)|`
Find |AB| if A = `[(3,-1),(2,1)]` and B = `[(3,0),(1,-2)]`
If A is square matrix of order 3 then |kA| is
The value of `|(5,5,5),(4x,4y,4z),(-3x,-3y,-3z)|` is
The value of `|(x,x^2 - yz,1),(y,y^2-zx,1),(z,z^2-xy,1)|` is
If A = `|(cos theta,sin theta),(-sin theta,cos theta)|`, then |2A| is equal to
If Δ = `|(a_11,a_12,a_13),(a_21,a_22,a_23),(a_31,a_32,a_33)|` and Aij is cofactor of aij, then value of Δ is given by:
Evaluate the following determinant:
`|(a,h,g),(h,b,f),(g,f,c)|`
Without expanding evaluate the following determinant.
`|(1,a,b+c),(1,b,c+a),(1,c,a+b)|`
Evaluate the following determinant:
`|(4,7),(-7,0)|`
Evaluate the following determinants:
`|(1, i, 3),(i^3, 2, 5),(3, 2, i^4)|`
Find the value of x if `|(x,-1,2),(2x,1,-3),(3,-4,5)|` = 29
Find the value of x if `|(x,-1,2),(2x,1,-3),(3,-4,5)|` = 29
Evaluate the following determinant:
`|(a,h,g),(h,b,f),(g,f,c)|`
