Determinants questions
307 published questions with worked solutions.
- Consider the following system of equations : x + 2y – 3z = a, 2x + 6y – 11z = b, x – 2y + 7z = c, where a, b and c are real...
- The value of vmatrix (a+1)&(a+2)&a+2 (a+2)&(a+3)&a+3 (a+3)&(a+4)&a+4 vmatrix is
- The number of values of for which the system of equations : x + y + z = , x + 2 y + 3z = −1, x + 3 y + 5z = 4 is inconsistent, is
- Let S = n : 1 n 50 and n is odd . Let a S and A = vmatrix 1&0&a -1&1&0 -a&0&1 vmatrix . If _ a S ( adj A) = 100 , then is equal...
- The number of real values of , such that the system of linear equations 2x − 3y + 5z = 9 x + 3y − z = −18 3x - y + ( ^ 2 - | |)z...
- The number of (0, 4 ) for which the system of linear equations 3( 3 )x - y + z = 2 3( 2 )x + 4y + 3z = 3 6x + 7y + 7z = 9 has no...
- If the system of linear equations 8x + y + 4z = −2 x + y + z = 0 x - 3y = has infinitely many solutions, then the distance of the...
- The ordered pair (a, b), for which the system of linear equations 3x − 2y + z = b, 5x − 8y + 9z = 3, 2x + y + az = −1 has no...
- If + + =2 , then the system of equations x + (cos ) y + (cos ) z = 0, (cos ) x + y + (cos ) z = 0, (cos ) x + (cos ) y + z = 0...
- For the system of linear equations ax + y + z = 1, x + ay + z = 1, x + y + az = , which one of the following is NOT correct?
- Let S denote the set of all real values of such that the system of equations x+y+z=1, x+ y+z=1, x+y+ z=1 is inconsistent, then _...
- Let P = [a_ ij ] be a 3×3 matrix and let Q = [b_ ij ], where b_ ij = 2^ i+j a_ ij for 1 i, j 3. If the determinant of P is 2,...
- Which of the following values of satisfy the equation vmatrix (1+ )^2 & (1+2 )^2 & (1+3 )^2 (2+ )^2 & (2+2 )^2 & (2+3 )^2 (3+ )^2...
- Let P= bmatrix 3 & -1 & -2 2 & 0 & 3 & -5 & 0 bmatrix , where R . Suppose Q=[q_ ij ] is a matrix such that PQ=kI, where k R , k 0...
- The total number of distinct x R for which vmatrix x & x^2 & 1+x^3 2x & 4x^2 & 1+8x^3 3x & 9x^2 & 1+27x^3 vmatrix =10 is
- If f(x)= vmatrix (2x) & (2x) & (2x) - x & x & - x x & x & x vmatrix , then
- Let P be a matrix of order 3 3 such that all the entries in P are from the set -1,0,1 . Then, the maximum possible value of the...
- If A is a square matrix of order 3 and A=5, then what is [(2A)^ -1 ] equal to?
- Which of the following is correct in respect of the system of equations x+y+z=8, x-y+2z=6 and 3x-y+5z=k? 1. They have no...
- If A= bmatrix &2 2& bmatrix and (A^3)=125, then is equal to
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