Determinants questions
307 published questions with worked solutions.
- Let m and M be respectively the minimum and maximum values of vmatrix ^2x&1+ ^2x& 2x 1+ ^2x& ^2x& 2x ^2x& ^2x&1+ 2x vmatrix ....
- The sum of distinct values of for which the system of equations ( -1)x+(3 +1)y+2 z=0 ( -1)x+(4 -2)y+( +3)z=0 2x+(3 +1)y+3(...
- If _1, _2 and _1, _2 are the roots of the equation ax^2+bx+c=0 and px^2+qx+r=0 respectively and system of equations _1y+ _2z=0...
- If vmatrix 6i&-3i&1 4&3i&-1 20&3&i vmatrix =x+iy, then
- If ( 1) is a cube root of unity, then vmatrix 1&1+i+ ^2& ^2 1-i&-1& ^2-1 -i&-i+ -1&-1 vmatrix equals
- The value of the determinant vmatrix 1+i&1-i&i 1-i&i&1+i &1+i&1-i vmatrix , where i= -1 is
- If , are the roots of equation ax^2+bx+c=0, then the value of the determinant vmatrix 1& ( - )& ( - )&1& & &1 vmatrix , is
- Let , be the roots of ax^2+bx+c=0, and let ^n+ ^n=S_n for n 1. Then the value of the determinant vmatrix 3&1+S_1&1+S_2...
- If f : ℕ → ℤ is defined by f(n)= vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 & 3k(2k+1) & 3k(k+2)+1 vmatrix , k∈ℕ, and _ n=1...
- Consider the system of linear equations in x,y,z: x+2y+tz=0, 6x+y+5tz=0, 3x+t²y+f(t)z=0, where f : ℝ → ℝ is a differentiable...
- The sum of all possible values of θ∈[0,2π], for which the system of equations: x cos3θ−8y−12z=0, x cos2θ+3y+3z=0, x+y+3z=0 has a...
- Consider the matrices : A = bmatrix 2&-5 3&m bmatrix , B = bmatrix 20 bmatrix and X = bmatrix x bmatrix . Let the set of all m,...
- The values of α, for which vmatrix 1 & 32 & + 32 1 & 13 & + 13 2 + 3 & 3 + 1 & 0 vmatrix = 0, lie in the interval
- The maximum value of f(x)= vmatrix ^2x&1+ ^2x& 2x 1+ ^2x& ^2x& 2x ^2x& ^2x& 2x vmatrix , x is:
- Let (4x^2)+4-4(4^x)-32=0 have the solution x = 2. Then evaluating the determinant vmatrix 3&1&4 1&0&2 2&1&0 vmatrix gives :
- If x, y, z are in arithmetic progression with common difference d, x 3d, and the determinant of the matrix vmatrix 3&4 2&x 4&5...
- The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k^2 has no solution if k is equal to
- If |A^2- 1 2 |=( ^2 - 1 2 )^2 where A= bmatrix & - & bmatrix
- If A= bmatrix 2&3 0&-1 bmatrix , then the value of det(A^4) + det(A^ 10 – (Adj(2A))^ 10 ) is equal to ——
- Let the system of linear equations 4x + + 2z = 0 2x – y + z = 0 + 2y + 3z = 0, , R. has a non-trivial solution. Then which of the...
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