Question

Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original system by c (d) If a matris is in reduced row echelou fornu theu it is also in zow echelon form (e) The sum of two invertible matrices of the same size must be invertible (t) IE the linear system Ax b has a unique solution then the system Ax - e also has a unique solution for all e where A is an (n x n) matrix and b.c eR ) The linear combinattions (aivi +agva) and (bvi+bva) can only be equal if ab and (h) İf T : Rr: → Rm and T(qXtc2y)s c1T(x) +gT(y) for all scalars ci, e2 and all vectors x, y E R" then T is a matrix transformation i) Two eigenvectors corresponding to the same eigenvalues are always linearly independent G) If every eigenvalue of a matrix A has algebraic multiplicity one then A is diagonalizable

Answer 1

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