Linear Algebra - Study Mode
[#91] If the rank of a (5 × 6) matrix Q is 4, then which one of the following statements is correct?
Correct Answer
(A) Q will have four linearly independent rows and four linearly independent columns
[#92] Consider the following system of equations 2x 1 + x 2 + x 3 = 0 x 2 - x 3 = 0 x 1 + x 2 = 0 This system has
Correct Answer
(C) infinite number of solutions
[#93] Let A be an n × n matrix with rank r(0 < r < n). Then AX = 0 has p independent solutions, where p is
Correct Answer
(C) n - r
[#94] The maximum value of "a" such that the matrix [left( {x08egin{array}{*{20}{c}}
{ - 3}&0&{ - 2} \
1&{ - 1}&0 \
0&{ ext{a}}&{ - 2}
end{array}}
ight)] xa0 has three linearly independent real eigen vectors is
Correct Answer
(B) [frac{1}{{3sqrt 3 }}]
[#95] In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x
Correct Answer
(A) Augmented matrix [Pq] must have the same rank as matrix P