Without performing row operations or doing any other work gi

Without performing row operations (or doing any other work), give the reason that each of the following sets is not a basis for M_2, 2, the set of matrices of size 2 times 2. a. A = {[1 -1 0], [0 1 1 0], [-2 7 3 1], [1 0 0 1], [8 3 0 1]} (b.) B = {[1 2 3 4], [2 -3 7 0], [14 0 0 10]}

Solution

For A you will have 4 Equations with 5 variables so you will not have a solution so not a basis for M_2,2

Similarly in B you will have 4 Equations with 3 variables where again there are many solutions so not a basis for M_2,2

Note :: Easy spotting of answer is that it should be a square matrix since there are 4 Equations to be formed, there should be 4 matrices in the set to be basis for M_2,2