MATH-205 Midterm: Bates MATH 205 100705ross205exam
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Initials: suppose t and s are linear transformations and a and b are their corresponding matrices, where a and b are given below. Explain why you can"t form the composition, t s. Let cij denote the i-jth entry of the matrix of the composition s t . Sketch two non-zero, unequal vectors in r2 which are not linearly independent, or explain why there are none. Sketch three di erent non-zero vectors in r2 which span r2, or explain why there are none. 3 in all parts of this question, matrices are in m3,3. Does e2 e1 represent the same sequence of elementary row operations? (compute the two products. Give an example of a matrix in m2,2 which has four di erent, nonzero integer entries and which is not invertible. Give an example of a matrix in m2,2 which has four di erent, nonzero integer entries such that the inverse also has four di erent, nonzero integer entries.
