Algebra Matrices Mock Tests

Let A be a 3x3 matrix with real entries such that A + A^T = 0 (skew-symmetric) and det(A) = 0. If the entries of A are chosen from {-1, 0, 1}, the number of such matrices A is

The system of equations x + y + z = 1, x + 2y + 3z = 2, x + 3y + pz = 3 has infinitely many solutions when p equals:

Let S be the set of all 3 × 3 matrices with entries from {0, 1, 2} such that the sum of all entries in each row equals 2. The number of such matrices is:

Let T = {0, 1}. The number of 3 x 3 matrices with entries from T such that the sum of each row equals the sum of the corresponding column (R_i = C_i for i = 1, 2, 3) is equal to:

The number of 3 x 3 symmetric matrices with entries from {0, 1} is:

Let A be a 3x3 matrix. If A can be expressed as the sum of a symmetric matrix S and a skew-symmetric matrix T, then:

Let A be a 3x3 matrix with eigenvalues 1, 2, and 3. Which of the following is/are TRUE?

Let S = {1, 2, 3, ..., 10}. The number of 2×2 matrices with distinct entries from S such that the sum of each row equals 5 and the sum of each column equals 5, is