MATH 131 Midterm: MATH 131 UMass Amherst Umass_Exam2_2014
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0 (a) find a basis for im a. Spring 2005 (b) find a basis for ker a. (c) find rank a: let a = . 2 3 0 5 8 (a) find a basis for the image of a. (b) find a basis for the kernel of a. (c) find the rank and the nullity of a: let a = . 1 3 8 (a) determine whether the column vectors of a are dependent or independent. If they are dependent, exhibit a linear dependence relation among them. 1 1 1 1 1 (a) find a basis for im a. (b) find a basis for ker a. (c) compute: dim(im a), dim(ker a), rank a: consider the folowing four vectors in r4. Explain your answer: let a = . 4 (a) determine whether the column vectors of a are dependent or independent. If they are dependent, exhibit a linear dependence relation among them. (b) write the vector ~b = .
