Question

You are given the following set of 5 vectors from R4: 4. 7,s} = {<2,-3,4,-5),(1,-2,2,-3),(1, 2, 2, 1), (5,-3, 7,-6), (6, 7, 3, 7)}, S and 11,15, 1, 18) e R4. Form the augmented matrix a. Next, we will find the rref of the augmented matrix. Take turns going around the group in deciding what row operation to do next. All members of the group should do that operation. Check each other's work. Do not do the next row operation until everyone has the same answer from the previous step b. Just by looking at the rref, explain why b is in Span(S) Write down all the solutions x1, x2, ..., xs to: C. d. xivix2v2+ . .. +xsvs = b Identify the leading and free variables By setting the free variables to zero, find the simplest solution to the equation in (d) and write your answer by rewriting the equation above with the coefficients substituted in. The answer involves only two out of the five vectors in S e. Can we write b as a linear combination of only vi, v2, and Vs? If this is possible, give an example f. Hint: force x3 and x4 be both be zero. What will happen to x, x2, and x5? Can we write b as a linear combination of only V3. V4, and vs? If this is possible, give an example. g. Can we write b as a linear combination of only vi, V2, and Vs? If this is possible, give an example. h.

Linear algebra

need to solve d,e,f,g,h

Answer 1

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