Let A be an m n matrix, where m > n. (a) What is the rank of A if the Ax = 0 has

Q: Let A be an m n matrix, where m > n. (a) What is the rank of A if the Ax = 0 has

A is m*n matrix (a)Ax=0 , rankA=n by the rank theorem (b) since m>n then there exist rows , dimNulla=m-n , we know that if dimNulla=0 then A is linealy indp. therfore A is linearly dp.

ID: 3102877 • Letter: L

Question

Let A be an m n matrix, where m > n.
(a) What is the rank of A if the Ax = 0 has only the trivial solution?
(b) Show that the rows of A are linearly dependent.
(c) If 0 is a nontrivial linear combination of the rows
with coecients c1; : : : ; cm, then what can you say about
the row vector y = [c1 : : : cm]?

Let B be a p q matrix, where p < q.
(d) Show that Bx = 0 has a nontrivial solution.
(e) What is the nullity of B if the rows are linearly independent?
(Give answer in terms of p and q)

Can you please answer and show all steps?.......

Explanation / Answer

A is m*n matrix (a)Ax=0 , rankA=n by the rank theorem (b) since m>n then there exist rows , dimNulla=m-n , we know that if dimNulla=0 then A is linealy indp. therfore A is linearly dp.

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Let A be an m n matrix, where m > n. (a) What is the rank of A if the Ax = 0 has

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