The number of `3xx3` matrices `A` whose entries are either `0or1` and for which the system `A|[x], [y ],[z]|=|[1], [0],[0]|` has exactly two distinct solution is a. 0 b. `2^9-1` c. `168` d. `2`

The number of all possible matrices of order 3xx3 with each entry 0 or 1 is :

The value of k for which the system of equations x+ky-3z=0 , 3x+ky-2z=0, 2x+3y-4z=0 has a non -trivial solution is

The values of k in R for which the system of equations x+k y+3z=0,k x+2y+2z=0,2x+3y+4z=0 admits of nontrivial solution is a. 2 b. 5//2 c. 3 d. 5//4

Let A be the set of all 3 xx 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices in A is

Let A be the set of all 3xx3 skew-symmetri matrices whose entries are either -1,0,or1. If there are exactly three 0s three 1s, and there (-1)' s , then the number of such matrices is __________.

If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite solutions, then the value of a is, a. -3 b. -1 c. 0 d. 3

Let A be the set of all 3xx3 symmetric matrices all of whose either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices A in A for which the system of linear equations A[(x),(y),(z)]=[(1),(0),(0)] is inconsistent is : (A) less than 4 (B) at least 4 but less than 7 (C) at least 7 but less than 10 (D) at least 10

The real number k of for which the equation 2x^3+3x+k=0 has two distinct real roots in [0,1]

Find the number of all possible matrices of order 3xx3 with each entry 0 or 1. How many of these are symmetric ?

The number of values of k for which the equation x^(2)-3x+k=0 has two distinct roots lying in the interval ( 0 , 1 ) are