Let M be the matrix whose columns are v1, v2, 2v1 – v2, v1 + 2v2 in that order. Then the number of linearly independent solutions of the homogeneous system of linear equations Mx = 0 is __________.Correct answer is '2'. Can you explain this answer?

Question

Let M be the matrix whose columns are v1, v2, 2v1 &#8211; v2, v1 + 2v2 in that order. Then the number of linearly independent solutions of the homogeneous system of linear equations Mx = 0 is __________.Correct answer is '2'. Can you explain this answer?

Answer

Here dimension of row space of M or row rank of M is 2  as there 2 linearly independent rows.. and by fundamental theorem of algebra dimension of null space of M is 2  ... hence there is 2 linearly independent solution of given homogenous equation

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