Norms We will prove the formula for the Matrix 1-norm in this problem. Recall that by definition of the Matrix 1-norm, Ar jalli = max 14th Alla- trix and let A, represent the jth Let A be an Tn n ma column of A. (a) Write down the formula for Az using the column view of matrix-vector multi- plication. b) Now, using the triangle inequality, establish the bound, max 1SiSn (c) Find a vector x such that lAxlla the j for which the max occurs) llxlla maxi-j-n IA,11. (Assume you know (d) Combines the results of the previous parts along with the definition of the vec- tor 1-norm to show that 7 1SjSn (Recall that triangle inequality says that a+yll sll+11al