Question

Decide whether the following are true or false. No justification is needed for this problem. a. True or False? If A is an n x n diagonalizable matrix, then A has n distinct eigenvalues. b. True or False? If a matrix A has a row of all zeros then the equation Ax = 0 has non-trivial solutions. c. True or False? If A is an n x n diagonalizable matrix, then A is invertible. d. True or False? Let A and B be two n x n matrices with the same eigenvalues. Then, A is similar to B. e. True or False? If A is an n x n matrix and Ax = 0 has a non-trivial solution, then the columns of A span R^n. f. True or False? If A is an invertible matrix, then the row vectors of A are linearly independent. g. True or False? Let A is a 5 x 5 matrix such that the rank(A) = n - 3. Then 0 is an eigenvalue of A. h. True or False? Suppose S is a subspace of dimension 2 in R^3. Then every basis for R^3 can be reduced to a basis for S by removing one vector.

          Decide whether the following are true or false. No justification is needed for this problem.
a. True or False? If A is an n x n diagonalizable matrix, then A has n distinct eigenvalues.
b. True or False? If a matrix A has a row of all zeros then the equation Ax = 0 has non-trivial solutions.
c. True or False? If A is an n x n diagonalizable matrix, then A is invertible.
d. True or False? Let A and B be two n x n matrices with the same eigenvalues. Then, A is similar to B.
e. True or False? If A is an n x n matrix and Ax = 0 has a non-trivial solution, then the columns of A span R^n.
f. True or False? If A is an invertible matrix, then the row vectors of A are linearly independent.
g. True or False? Let A is a 5 x 5 matrix such that the rank(A) = n - 3. Then 0 is an eigenvalue of A.
h. True or False? Suppose S is a subspace of dimension 2 in R^3. Then every basis for R^3 can be reduced to a basis for S by removing one vector.

Decide whether the following are true or false. No justification is needed for this problem.
a. True or False? If A is an n x n diagonalizable matrix, then A has n distinct eigenvalues.
b. True or False? If a matrix A has a row of all zeros then the equation Ax = 0 has non-trivial solutions.
c. True or False? If A is an n x n diagonalizable matrix, then A is invertible.
d. True or False? Let A and B be two n x n matrices with the same eigenvalues. Then, A is similar to B.
e. True or False? If A is an n x n matrix and Ax = 0 has a non-trivial solution, then the columns of A span R^n.
f. True or False? If A is an invertible matrix, then the row vectors of A are linearly independent.
g. True or False? Let A is a 5 x 5 matrix such that the rank(A) = n - 3. Then 0 is an eigenvalue of A.
h. True or False? Suppose S is a subspace of dimension 2 in R^3. Then every basis for R^3 can be reduced to a basis for S by removing one vector.

Added by Terri F.

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