Give a proof for the Consistency Theorem in two steps: (A linear system Ax = b is consistent if and only if b can be written as a linear combination of the column vectors of A.) I) Prove that if b could be written as a linear combination of the column vectors of A, the linear system Ax=b is consistent by writing b as b= a1x1+a2x2+a3x3+...+anxn and examine x (a1) (a2) (a3) II) Prove that the linear system Ax=b is consistent by rewriting Ax

What is this inequality notation? t is less then or equal to 2

Last year, a state university received 3,560 applications from boys. of those applications, 35 percent were from boys who lived in other states. part a)how many applications did the university receive from boys who lived in other states? part b)applications to the university from boys represented 40percent of all applications. how many applications did the university receive in all? i don't how to do part b so me and plz tell how you got your answer

The volume of gas a balloon can hold varies directly as the cube of its radius. imagine a balloon with a radius of 3 inches can hold 81 cubic inches of gas. how many cubic inches of gas must be released to reduce the radius down to 2 inches?