Determinants questions
307 published questions with worked solutions.
- If (a-b)(b-c)(c-a)=2 and abc=6, then what is the value of vmatrix a&b&c ^2&b^2&c^2 ^3&b^3&c^3 vmatrix ?
- Under which of the following conditions does the determinant vmatrix a&b&c &c&a &a&b vmatrix vanish? 1. a+b+c=0 2....
- If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C=A+B?
- Consider the determinant = vmatrix a_ 11 &a_ 12 &a_ 13 _ 21 &a_ 22 &a_ 23 _ 31 &a_ 32 &a_ 33 vmatrix . If a_ 13 =yz, a_ 23 =zx,...
- What is the sum of the roots of the equation vmatrix 0&x-a&x-b 0&0&x-c +b&x+c&1 vmatrix =0?
- If a, b, c are in AP, then what is vmatrix x+1&x+2&x+3 +2&x+3&x+4 +a&x+b&x+3 vmatrix equal to?
- If A= bmatrix 1 2 3 bmatrix , then what is the value of (I+AA'), where I is the 3 3 identity matrix?
- If A, B and C are square matrices of order 3 and (BC)=2 (A), then what is the value of (2A^ -1 BC)?
- If vmatrix x^2+3x & x-1 & x+3 x+1 & -2x & x-4 x-3 & x+4 & 3x vmatrix =ax^4+bx^3+cx^2+dx+e, then what is the value of e?
- If all elements of a third order determinant are equal to 1 or -1, then the value of the determinant is :
- If A_k= bmatrix k-1&k -2&k+1 bmatrix , then what is (A_1)+ (A_2)+ (A_3)+ + (A_ 100 ) equal to?
- For what value of n is the determinant vmatrix C(9,4)&C(9,3)&C(10,n-2) (11,6)&C(11,5)&C(12,n) (m,7)&C(m,6)&C(m+1,n+1) vmatrix =0...
- If ABC is a triangle, then what is the value of the determinant vmatrix C& B&0 A&0& B 0& (B+C)& C vmatrix ?
- If a, b, c are the sides of triangle ABC, then what is vmatrix a^2&b A&c A A&1& A A& A&1 vmatrix equal to?
- If in a triangle ABC, ^3A+ ^3B+ ^3C=3 A B C, then what is the value of the determinant vmatrix a&b&c &c&a &a&b vmatrix ; where a,...
- If D_n= vmatrix n&20&30 ^2&40&50 ^3&60&70 vmatrix then what is the value of _ n=1 ^ 4 D_n?
- If = vmatrix a & b & c d & e & f g & h & i vmatrix and A, B, C, D, G are the cofactors of the elements a, b, c, d, g...
- Consider the following statements in respect of the determinant = vmatrix k(k+2) & 2k+1 & 1 2k+1 & k+2 & 1 3 & 3 & 1 vmatrix I....
- If A^2+B^2+C^2=0, then what is the value of the following? vmatrix 1 & C & B C & 1 & A B & A & 1 vmatrix
- If is a non-real cube root of unity, then what is a root of the following equation? vmatrix x+1 & & ^2 & x+ ^2 & 1 ^2 & 1 & x+...
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