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Posted: **Thu May 12, 2022 6:28 am**

: N Question 2 Umn 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 (15.07 KiB) Viewed 25 times

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: N Question 2 Umn Sums Let M Be An M X N Matrix With Real Entries Assume That The Entries In Each Column Of M Add Up To 3 (6.36 KiB) Viewed 25 times

n Question 2 umn 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:R" R", TMis 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.e, contains a non-zero vector.