Determinants questions
307 published questions with worked solutions.
- If vmatrix x+1&x&x &x+ &x &x&x+ ^2 vmatrix = 9 8 (103x+81), then , 3 are the roots of the equation
- Let D_k= vmatrix 1&2k&2k-1 &n^2+n+2&n^2 &n^2+n&n^2+n+2 vmatrix . If _ k=1 ^nD_k=96, then n is equal to __________.
- If the system of equations 2x + y – z = 5, 2x – 5y + = , x + 2y – 5z = 7 has infinitely many solutions, then ( + )^2+( - )^2 is...
- Let the determinant of a square matrix A of order m be m – n, where m and n satisfy 4m + n = 22 and 17m + 4n = 93. If det(n...
- Let the system of linear equations –x + 2y – 9z = 7, –x + 3y + 7z = 9, –2x + y + 5z = 8, –3x + y + 13z = has a unique solution x...
- If the system of equations x + 2y + 3z = 3, 4x + 3y – 4z = 4, 8x+4y- z=9+ has infinitely many solutions, then the ordered pair (...
- Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations x + y + z = 1,...
- Let be a root of the equation (a-c)x^2+(b-a)x+(c-b)=0 where a, b, c are distinct real numbers such that the matrix bmatrix ^2& &1...
- Let A be a symmetric matrix such that |A| = 2 and pmatrix 2&1 3& 3 2 pmatrix A = pmatrix 1&2 & pmatrix . If the sum of the...
- For , R suppose the system of linear equations x – y + z = 5, 2x + 2y + z = 8, 3x – y + 4z = Has infinitely many solutions. Then...
- For the system of linear equations x + y + z = 6, + + 7z = 3, x + 2y + 3z = 14, which of the following is NOT true?
- l, m, n are the p^ th , q^ th and r^ th term of a G.P. all positive, then vmatrix l & p & 1 m & q & 1 n & r & 1 vmatrix equals
- If a > 0 discriminant of ax^2 + 2bx + c is -ve, then vmatrix a & b & ax+b & c & bx+c +b & bx+c & 0 vmatrix is
- If the system of linear equations x + 2ay + az = 0 x + 3by + bz = 0 x + 4cy + cz = 0 has a non-zero solution, then a, b, c
- If vmatrix a & a^2 & 1 + a^3 & b^2 & 1 + b^3 & c^2 & 1 + c^3 vmatrix = 0 and vectors (1, a, a^2), (a, b, b^2) and (a, c, c^2) are...
- If a_1, a_2, a_3, , a_n, are in G.P., then the value of the determinant vmatrix a_n & a_ n+1 & a_ n+2 a_ n+3 & a_ n+4 & a_ n+5 a_...
- The system of equations x + y + z = - 1, x + y + z = - 1, x + y + z = - 1 has no solution, if is
- If a^2 + b^2 + c^2 = -2 and f(x) = vmatrix 1 + a^2x & (1 + b^2)x & (1 + c^2)x (1 + a^2)x & 1 + b^2x & (1 + c^2)x (1 + a^2)x & (1...
- Let A = bmatrix 5 & 5 & 0 & & 5 0 & 0 & 5 bmatrix . If |A^2| = 25, then | | equals
- If D = vmatrix 1 & 1 & 1 1 & 1 + x & 1 1 & 1 & 1 + y vmatrix for x 0, y 0 then D is
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