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 26 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 2 (5.11 KiB) Viewed 26 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 3 (6.36 KiB) Viewed 26 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.
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