Check the boxes next to the statements that are true. O A vector is a linear com

Question

Check the boxes next to the statements that are true. O A vector is a linear combination of the columns of a matrix A if and only if the equation Az = b has at least one solution. ave a pivot position in every row. O If the columns of an m x n matrix A span R'", then the equation Ax = b is consistent for each b in Rm OThe first entry in the product Ac is a sum of products. O The equation Ax b is consistent if the augmented matrix | A-] has a pivot position in every row The equation Ax = b is referred to as a vector equation.

Explanation / Answer

1st four are true

option 1 True, the equation Ax=b has the same solutions set as the equation xa+xa+...+x(subn)a(subn)=b

option 2True, because if A is an mxn matrix and if the equation Ax=b is inconsistent for some b in R^m,

option 3 True,because the columns mxn of A span R^m, then the equation Ax=b has a solution for each b in R^m.

option 4 True,because the first entry in Ax* is the sum of products of corresponding entries in x and the first entry in each column of A.

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