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1. (10 points) True/False questions. No justification necessary. (a) True False The matrix 1 01 1 0 17 01 10 0 0 0 0 0 01 1 0 0 0 0 0 0 (b) True is in row reduced echelon form. False If A E MA(R) has eigenvalues -1, 2, and 6 with dim( E-1) + dim(E2) + dim( E6) = 3, then A is diagonalizable. (c) True False The matrix 10 0 021 0131 0 0 0 01 6 1 0171 0 0 0 0 1 is invertible. (d) True False dim ( Mn (R) ) = n. (e) True False If v1, v2, v3 are nonzero vectors such that vi + 7v2 - 403 = 0, then V1; V2, v3 are linearly dependent. (f) True False If v1, V2, V3, v4 are linearly independent in R4, then they must span (g) True False If [0 1 3 -22] is is in El-, then [0 1 3 + 2i] is in Eiti. (h) True False If r1, r2, ..., rk is any list of scalars, then there is a matrix A with eigenvalues r1, 12, . . ., k. (i) True False If the only eigenvalue of a matrix is zero, then the matrix must be the zero matrix. (j) True False The functions e2r, e2t cos(2x), e2t sin(2x) are linearly independent