MATH 325 CCSF Linear Algebra Vectors Matrixes Eigenvalues & Eigenvectors Exam Practice


Help me examine for my Algebra assort. I’m accumulate and don’t interpret.

1. Determine if the vectors   1 −2 3   ,   3 2 1  ,   5 6 −1   are linearly refractory or linearly trusting. Please interpret your counterpart. 2. Let A be the matrix   1 2 −3 1 0 2 −3 4 6  . For which vectors b does the equation Ax = b enjoy a disentanglement? 3. Does there exist a 3×3 matrix A that satisfies A2 = −I (where I denotes the personality matrix)? Hint: if A satisfies A2 = −I, what would det(A) be similar to? 4. If A is a 9 × 4 matrix, what is the lowest reckon of easy variables the equation AT x = 0 can enjoy? Please interpret. 5. Find eigenvalues and eigenvectors of the matrix −14 12 −20 17 . 6. Give an stance of a 2 × 2 matrix A and 2− dimensional vectors u and v such that u and v are orthogonal to each other, but the vectors Au and Av are not orthogonal to each other. 7. Apply Gram-Schmidt rule to the vectors   1 −3 5   ,   2 2 1  . 8. Let A be an n × n matrix. Suppose that for some vector b the equation Ax = b has further than one disentanglement. Interpret why A is not an invertible matri