1. Rank of the matrix A =
Hence rank of A=3
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2. A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is
A must be invertible
b must be linearly depended on the columns of A
b must be linearly independent of the columns of A
None of these
3. The system of linear equations
(4d - 1)x +y + z = 0
- y + z = 0
(4d - 1) z = 0
has a non-trivial solution, if d equals
=> -(4d-1)2 = 0
=> d = 1/4
4. The rank of a 3 x 3 matrix C (= AB), found by multiplying a non-zero column matrix A of size 3 x 1 and a non-zero row matrix B of size 1 x 3, is
5. If A and B are square matrices of size n x n, then which of the following statement is not true?
det. (AB) = det (A) det (B)
det (kA) = kn det (A)
det (A + B) = det (A) + det (B)
det (AT) =1/det (A-1)
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