5 points) let a = 2 0 6 ?1 8 5 1 ?2 1 and b = 10 3 3 and let w be the set of all linear combinations of the columns of a. (a) is b in w ? (b) show that the third column of a is in w .

Question

5 points) let a = 2 0 6 ?1 8 5 1 ?2 1 and b = 10 3 3 and let w be the set of all linear combinations of the columns of a. (a) is b in w ? (b) show that the third column of a is in w .

Accepted Answer

Final answer:To determine if vector b is in the set of all linear combinations of the columns of matrix a, solve the equation a*x = b. To show that thethird column of matrix a is in the set,solve theequation a*x = c.Explanation:To determine if vectorbis in the set of all linear combinations of the columns of matrixa(denoted asw), we need to check if it is possible to expressbas a linear combination of the columns ofa. We can do this by solving the equationa*x=bfor vectorx, whereais the matrix of column vectors fromaandbis vectorb. If a solution exists,bis inw. To show that the third column of matrixais inw, we can express it as a linear combination of the columns ofaby solving the equationa*x=c, whereais the matrix of column vectors fromaandcis the third column ofa. If a solution exists, the third column is inw.Learn more about Linear combinations here:brainly.com/question/35637422#SPJ11...

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5 points) let a = 2 0 6 ?1 8 5 1 ?2 1 and b = 10 3 3 and let w be the set of all linear combinations of the columns of a. (a) is b in w ? (b) show that the third column of a is in w .

5 points) let a = 2 0 6 ?1 8 5 1 ?2 1 and b = 10 3 3 and let w be the set of all linear combinations of the columns of a. (a) is b in w ? (b) show that the third column of a is in w .