Home
Class 12
MATHS
If A,B and C are square matrices of orde...

If A,B and C are square matrices of order n and det (A)=2, det(B)=3 and det ©=5, then find the value of 10det `(A^(3)B^(2)C^(-1)).`

Text Solution

Verified by Experts

Given , `|A|=2,|B|=3 and |c|=5.`
Now, 10det `(A^(3)B^(2)C^(-1))=10xx|A^(3)B^(2)C^(1)|`
`=10xx|A^(3)|xx|B^(2)|xx|C^(-1)|=10xx|A^(3)|xx|B^(2)|xx|C|^(-1)`
`=(10xx|A^(3)|xx|B^(2)|)/(|C|)=(10xx2^(3)xx3^(2))/(5)=144`
Promotional Banner

Similar Questions

Explore conceptually related problems

If A , B and C are square matrices of same order, then AB=AC always implies that B=C.

If A and B are square matrices of same order then (A^(-1)BA)^(n) = ………… , n inN .

If A and B are matrices of order 3 and |A| = 5 , |B| = 3, then |3AB| = 27xx5xx3=405 .

If A and B are two matrices of the order 3xxmand3xxn , respectively , and m=n , then the order of matrix (5A-2B) is ……….

Let A and B be square matrices of the order 3xx3 . Is (AB)^(2)=A^(2)B^(2) ? Given reasons .

If A is an invertible matrix of order 2, then det (A^(-1)) is equal to …….

If a+b+c=3 and agt0,bgt0,cgt0 then the greatest value of a^(2)b^(3)c^(2) is

If |a|=1,|b|=3 and |c|=5 , then the value of [a-b" "b-c" "c-a] is

If x^2+3x+5=0 and a x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+c .

Assume X, Y, Z, W and P Are Matrices of Order 2 x n, 3 x k, 2 x p,N x 3 and Respectively. If n =p , then the order of the matrix 7X-5Z is : (A) pxx2 (B) 2xxn (C ) nxx3 (D) pxxn