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Problem 1 (30 points) True or False (3 points for correct answer, 1 point for blank):
A matrix in RREF has the same solution set as the original matrix. 2. If V is a vector space, then every basis of V has the same size. 3. If v, w are in R3, then the Span(v, w) is a subspace of R3. 4. The dimension of a vector space is the number of elements in the vector space. 5. If the matrix product AB is defined then the number of rows of A is equal to the number of columns of B. 6. An eigenvalue can have more than one eigenvector. 7. The multiplicity of an eigenvalue cannot be greater than the dimension of the corresponding eigenspace.
The eigenspaces of two distinct eigenvalues are orthogonal to eachother. 9. If T : R5 R4 is a linear transformation, then T is not 1-1. 10. There exist v1, v2 and v3 in R4, which are linearly independent.
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