#1) Find the general solution of the system whose augmented matrix is given below. 10 -3 0 -8 4 0 1 6 -1 07 0 0 0 10 0 0 0 0 0 0 #2) A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Suppose that such a system happens to be consistent. Explain why there must be an infinite number of solutions. #3) Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. 2 26 #4) Let T: R2 -+R be a linear transformation such that T (X1,*2) = (x, +*2. 3x, + 6*2) . Find x such that T(x) = (3, -3). #5) -2 -7 - 22 Let A = 3 5 11 . Find the third column of A without computing the other two columns. 3 10#6) An economy is based on three sectors-agriculture, manufacturing, and services. For each unit of output, agriculture requires inputs of 0.20 unit from agriculture, 0.40 unit from manufacturing, and 0.20 unit from services. For each unit of output, manufacturing requires inputs of 0.30 unit from agriculture, 0.20 unit from manufacturing, and 0.20 unit from services. For each unit of output, services requires 0.20 unit from agriculture, 0.30 unit from manufacturing, and 0.30 unit from services. Determine the production levels needed to satisfy a final demand of 0 units for agriculture, 40 units for manufacturing, and 0 units for services. #7) Compute the determinant using a cofactor expansion across the first row. Also compute the determinant by a cofactor expansion down the second column. - 6 #8) Find the area of the parallelogram with vertices (-1, -2), (4, 5), (8, -4), and (13, 3). #9) Let H be the set of all vectors of the form 0 Show that H is a subspace of R3. -5t #10) If the nullity of a 4 x 6 matrix A is 3, what are the dimensions of the column and row spaces of A? #11) Write a paragraph or two about a concept or particular problem you've run into in this course that gave you trouble at first, but you now feel you understand well. How did you get the concept to finally "click"? #12) What application of linear algebra from the course have you found most interesting so far? How would you describe that application to a friend of your who hasn't taken linear algebra, but is considering doing so