MATH 131 Midterm: MATH 131 UMass Amherst Umass_Exam2_2011
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Instructions: put your name in the blanks above. Put your nal answers to each question in the designated spaces. If they are dependent, exhibit a linear dependence relation among them. 2 (b) write the vector ~b = . As a linear combination of the vectors ~v1, ~v2, ~v3. 2 has the matrix as its row-reduced echelon form: 10 points the matrix a = 0 (a) find a basis for the image of a. (b) find a basis for the kernel of a. (c) compute: rank a , dim (ker a) , dim (im a) , dim (ker a) = Spring 2005 (a) find the least squares solution ~x of the inconsistent system a~x = ~b, where. 2 (b) use your answer to part (a) to nd the projection of ~b onto the image of a. (c) determine the error ||~b a~x ||. Spring 2005: 14 pts apply the gram-schmidt process to the vectors.
