Matrices & Determinants Questions

If x, y, z are in A.P, lying between 1 and 9, and x51, y41 and z31 are three digit numbers, then value of is

If matrix A = , where a, b, c are numbers such that abc = 1, a + b + c = 1 & A.A. Find the value of a.

If a, b, c are all different and find the value of abc (ab + bc + ca) – (a + b + c) is

If A is a 3 × 3 order matrix, such that |A| = 2 then value of |adj(adj(adj(adj A)))| = a then the value of 2a + is equal to (where a is prime number)

Let A = where is a complex cube root of unity, B = and A, where k = ....

If A = [aij] is a skew-symmetric matrix of order n, then aii is equal to: (1) 0 for some i (2) 0 for all i = 1, 2, ..., n (3) 1 for some i (4) 1 for all i = 1, 2, ......, n

If A = then the value of the determinant |A – 5I| is

If M = and M, then

If the lines px + qy + r = 0, rx + py + q = 0, and qx + ry + p = 0 are concurrent then the value of p + q + r is, (where p, q, r are distinct)

The value of A, is

If the matrix B = , then B is equal to

If , Adj A = , then

If a matrix A is such that , then its inverse is

If the system of equation has infinitely many solutions, then-

If A and B are square matrices of order 3 such that and , then value of is equal to

Let and find abc + abd + bcd + acd.

A skew-symmetric matrix A satisfies the relation , where I is a unit matrix. Then A is

If , then the system of equations x + (cos )y + (cos )z = 0, (cos )x + y +(cos )z = 0, (cos )x + (cos )y + z = 0 has

If = A + Bx + , then B is equal to

Let be a matrix, then is equal to

Let M be a 3 3 matrix satisfying , and Then the sum of the diagonal entries of M, is:

The value of the determinant is

If A and B are symmetric matrices of the same order, then:

If and , (i = 1, 2, 3, 4) then number of different possible real value of is

If , then x+y+z+w=