MATH-205 Midterm: Bates MATH 205 111105jayawant205exam
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Use properties of determinants to compute: (a) det 4b (b) det c where c is obtained from a by interchanging rows 1 and 3 (c) det at b t (d) det (ab) 1 if ab is invertible. Otherwise, explain why ab is not invertible: (6 points) determine if each of the following sets is a subspace of the appropriate vector space. If so, nd a basis and dimension of the subspace. (a) let w = 4b + 4c + 2d a + b + 4c + d. : a, b, c, d are real numbers. Is w a subspace of r4? (b) let w = a + b. Explain: (8 points) let a = . If possible, nd a basis b for r3 consisting of the eigenvectors of a and write the. If such a basis does not exist, explain why. (the eigenvalues of a are 15 and. And t : r3 r3 be the linear transformation given by.
