Determinants questions
307 published questions with worked solutions.
- If vmatrix a & -b & a-b-c -a & b & -a+b-c -a & -b & -a-b+c vmatrix -kabc=0 (a 0, b 0, c 0) then what is the value of k?
- If x= a b-c , y= b c-a , z= c a-b then what is the value of the following? vmatrix 1 & -x & x 1 & 1 & -y 1 & z & 1 vmatrix
- The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 2 matrix such that the trace of A is 3...
- For any 3 3 matrix M, let |M| denote the determinant of M. Let E = bmatrix 1 & 2 & 3 2 & 3 & 4 8 & 13 & 18 bmatrix , P = bmatrix...
- For any 3 3 matrix M, let |M| denote the determinant of M. Let I be the 3 3 identity matrix. Let E and F be two 3 3 matrices such...
- Let , and be real numbers. Consider the following system of linear equations x + 2y + z = 7 x + z = 11 2x - 3y + z = Match each...
- Let S = A = pmatrix 0 & 1 & c 1 & a & d 1 & b & e pmatrix : a, b, c, d, e 0, 1 and |A| -1, 1 , where |A| denotes the determinant...
- Let A = bmatrix 4 & -2 & bmatrix . If A^ 2 + A + 18I = 0, then det(A) is equal to _____ .
- Consider a matrix A = bmatrix & & ^ 2 & ^ 2 & ^ 2 + & + & + bmatrix , where , , are three distinct natural numbers. If...
- Let f(x) = |a −1 0; ax a −1; ax^ 2 ax a|, a R. Then the sum of the square of all the values of a, for which 2f'(10) - f'(5) + 100...
- Let the system of linear equations x + 2y + z = 2, x + 3y - z = , - x + y + 2z = - be inconsistent. Then is equal to :
- The positive value of the determinant of the matrix A, whose Adj(Adj(A)) = bmatrix 14 & 28 & -14 -14 & 14 & 28 28 & -14 & 14...
- If the system of linear equations 2x - 3y = + 5, x + 5y = + 1, where , , R has infinitely many solutions, then the value of |9 +...
- If the system of linear equations 2x + 3y − z = −2, x + y + z = 4, x - y + | |z = 4 - 4 where R, has no solution, then
- Let p and p + 2 be prime numbers and let = |p!, (p + 1)!, (p + 2)!; (p + 1)!, (p + 2)!, (p + 3)!; (p + 2)!, (p + 3)!, (p + 4)!|....
- A is a square matrix of order 3 such that its determinant is 4. What is the determinant of its transpose?
- If A is a square matrix of order n>1, then which one of the following is correct?
- Let S be the set of all values of [- , ] for which the system of linear equations x + y + 3z = 0, –x + y + 7z = 0, x + y + (tan...
- Let S be the set of values of for which the system of equations 6 – 3y + 3z = 4 ^2, 2x + 6 + 4z = 1, 3x + 2y + 3 = has no...
- If the system of linear equations 7x + 11y + = 13; 5x + 4y + 7z = ; 175x + 194y + 57z = 361 has infinitely many solutions, then +...
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