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
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A.
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A must be invertible
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B.
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b must be linearly depended on the columns of A
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C.
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b must be linearly independent of the columns of A
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D.
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None of these
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Answer
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4: |
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
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Answer
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Answer & ExplanationAnswer: Option B
Explanation :
The system of homogeneous linear equations has a non-trivial solution if
=> -(4d-1)2 = 0
=> d = 1/4
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5: |
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
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Answer
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Answer & ExplanationAnswer: Option B
Explanation :
∴ |
C |
= |
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a1a2 |
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a1b2 |
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a1c2 |
b1a2 |
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b1b2 |
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b1c2 |
c1a1 |
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c1b2 |
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c1c2 |
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