Let B be a 5 x4 matrix with real entries such that the space of all solutions of the linear systemis given by(Here Mt denotes the transpose ofM), then the rank of B is equal to _______ .Correct answer is '3'. Can you explain this answer?

Question

Answer

Now (1 + 2s , 2 + 3s, 3 + 4s, 4 + 5s) = 1(1,2, 3, 4) + s(2, 3, 4, 5)

Here { ( 1 , 2, 3, 4), ( 2, 3, ,4 ,5 ) } be a L.l. set, which spanned ω

⇒ dim ω = 2

∴ The no. of linearly independent solution of the given non - homogeneous system of equation is 2.

Answer

Now (1 + 2s , 2 + 3s, 3 + 4s, 4 + 5s) = 1(1,2, 3, 4) + s(2, 3, 4, 5)

Here { ( 1 , 2, 3, 4), ( 2, 3, ,4 ,5 ) } be a L.l. set, which spanned ω

⇒ dim ω = 2

∴ The no. of linearly independent solution of the given non - homogeneous system of equation is 2.

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