Determinants questions
307 published questions with worked solutions.
- Let , , be the real roots of the equation, x^3+ax^2+bx+c=0, (a,b,c R and a,b 0). If the system of equations (in, u, v, w) given...
- The value of k , for which the following system of linear equations 3x – y + 4z = 3, x + 2y – 3z = –2, 6x + 5y + kz = –3, has...
- Let A=[a_ ij ] be a 3×3 matrix, where a_ ij = cases 1, & if i=j -x, & if |i-j|=1 2x+1, & otherwise cases . Let a function f : R R...
- Let a, b, c, d be in arithmetic progression with common difference . If vmatrix x+a-c&x+b&x+a -1&x+c&x+b -b+d&x+d&x+c vmatrix =2,...
- Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The probability that such...
- For the system of linear equations : x – 2y = 1, x – y + kz = –2, ky + 4z = 6, k R, consider the following statements : (A) The...
- The system of linear equations 3x – 2y – kz = 10, 2x – 4y – 2z = 6, x + 2y – z = 5m is inconsistent if :
- Let P= bmatrix 3&-1&-2 2&0& 3&-5&0 bmatrix , where R. Suppose Q = [q_ ij ] is a matrix satisfying PQ = kI_3 for some non-zero k...
- The determinant = vmatrix a&b&a +b &c&b +c +b&b +c&0 vmatrix is equal to zero, if
- If a,b,c be respectively the p^ th , q^ th and r^ th terms of a HP., then = vmatrix bc&ca&ab &q&r 1&1&1 vmatrix equals
- Let f(X)= vmatrix ^2x&-2+ ^2x& 2x 2+ ^2x& ^2x& 2x ^2x& ^2x&1+ 2x vmatrix , x [0, ]. Then the maximum value of f(X) is equal to...
- Let A = pmatrix [x+1]&[x+2]&[x+2] [x] &[x+3]&[x+3] [x] &[x+2]&[x+4] pmatrix , where [t] denotes the greatest integer less than or...
- If the following system of linear equations 2x + y + z = 5, x – y + z = 3, x + y + az = b has no solution, then :
- The following system of linear equations 2x + 3y + 2z = 9, 3x + 2y + 2z = 9, x – y + 4z = 8
- If the system of equations kx + y + 2z = 1, 3x – y – 2z = 2, –2x – 2y – 4z = 3 has infinitely many solutions, then k is equal...
- The values of a and b, for which the system of equations 2x + 3y + 6z = 8, x + 2y + az = 5, 3x + 5y + 9z = b has no solution, are...
- Let M = A= pmatrix a&b &d pmatrix :a,b,c,d 3, 2, 1,0 Define f:M Z, as f(A) = det(A), for all A , where Z is set of all integers....
- Two fair dice are thrown. The numbers on them are taken as and , and a system of linear equations x + y + z = 5, x + 2y + 3z = ,...
- Let A be a 3 × 3 real matrix. If det(2Adj(2 Adj(Adj(2A)))) = 2^ 41 , then the value of det(A^2) equal________.
- Let (0, 2 ). If the system of linear equations (1+ ^2 )x+ ^2 y+4 3 z=0, ^2 x+(1+ ^2 )y+4 3 z=0, ^2 x+ ^2 y+(1+4 3 )z=0 has a...
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