Determinants questions
307 published questions with worked solutions.
- If f(x) = vmatrix 1 & x & x+1 2x & x(x-1) & x(x+1) 3x(x-1) & x(x-1)(x-2) & x(x^2-1) vmatrix then f(100) is equal to
- The value of vmatrix i^m & i^ m+1 & i^ m+2 i^ m+5 & i^ m+4 & i^ m+3 i^ m+6 & i^ m+7 & i^ m+8 vmatrix , where i = -1 , is
- If _1 = vmatrix 7 & x & 2 -5 & x+1 & 3 4 & x & 7 vmatrix , _2 = vmatrix x & 2 & 7 x+1 & 3 & -5 x & 7 & 4 vmatrix then _1 - _2 = 0...
- If _1 = vmatrix 10 & 4 & 3 17 & 7 & 4 4 & -5 & 7 vmatrix , _2 = vmatrix 4 & x+5 & 3 7 & x+12 & 4 -5 & x-1 & 7 vmatrix such that...
- Let vmatrix ^2+3 & -1 & +3 +1 & -2 & -4 -3 & +4 & 3 vmatrix = p ^4 + q ^3 + r ^2 + s + t be an identity in , where p, q, r, s, t...
- Let vmatrix 1+x & x & x^2 x & 1+x & x^2 x^2 & x & 1+x vmatrix = ax^5+bx^4+cx^3+dx^2+ x+ be an identity in x, where a, b, c, d, ,...
- Using the factor theorem it is found that b+c, c+a and a+b are three factors of the determinant vmatrix -2a & a+b & a+c b+a & -2b...
- If the determinant vmatrix 2x & ^2 x & 4x ^2 x & 2x & ^2 x 4x & ^2 x & 2x vmatrix is expanded in powers of x then the constant...
- If (x)= vmatrix 1 & x & 1- x 1+ x & x & 1+ x- x x & x & 1 vmatrix then _0^ /2 (x) ,dx is equal to
- If i= -1 and [4] 1 = , , , then vmatrix & & & & & & & & & & & & vmatrix is equal to
- The roots of vmatrix x & a & b & 1 & x & b & 1 & & x & 1 & & & 1 vmatrix =0 are independent of
- The value of vmatrix 1&0&0&0&0 2&2&0&0&0 4&4&3&0&0 5&5&5&4&0 6&6&6&6&5 vmatrix is
- If vmatrix b^2+c^2 & ab & ac ba & c^2+a^2 & bc ca & cb & a^2+b^2 vmatrix is the square of a determinant of the third order then...
- The system of equations ax+4y+z=0, bx+3y+z=0, cx+2y+z=0 has nontrivial solutions if a, b, c are in
- The system of equations cases 2x-y+z=0 x-2y+z=0 x-y+2z=0 cases has infinite number of nontrivial solutions for
- The equations x+y+z=6, x+2y+3z=10, x+2y+mz=n give infinite number of values of the triplet (x,y,z) if
- If the system of equations cases ax+by+c=0 bx+cy+a=0 cx+ay+b=0 cases has a solution then the system of equations cases...
- Let _1, _2, _3, , _k be the set of third-order determinants that can be made with the distinct nonzero real numbers a_1,a_2,a_3,...
- vmatrix x^2 & (y+z)^2 & yz y^2 & (z+x)^2 & zx z^2 & (x+y)^2 & xy vmatrix is divisible by
- The equation vmatrix 1&x&x^2 ^2&1&x &x^2&1 vmatrix =0 has
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