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Question 2 Column sums Let M be an m x n matrix with real entries. Assume that the entries in each column of M add up to
Posted: Thu May 05, 2022 6:42 pm
by answerhappygod
- Question 2 Column Sums Let M Be An M X N Matrix With Real Entries Assume That The Entries In Each Column Of M Add Up To 1 (48.46 KiB) Viewed 36 times
Question 2 Column sums Let M be an m x n matrix with real entries. Assume that the entries in each column of M add up to zero. (a) Show that the linear transformation T: RR", →→→ Mi is not surjective. Hint: You might like to play around with some small examples, e.g. for m = 2 or m = 3. (b) Find a non-zero vector in the null space of the transpose matrix MT. Justify your answer. (c) Assume now that m = n. Show that the null space of M is non-trivial, i.c, contains a non-zero vector.