Question 1) Consider the following matrix: A = | 1 2 1 | | 2 4 1 | | 1 2 2 | a) Compute the kernel and the nullity of A. Does A have a trivial kernel? b) What is the rank of A? c) Find a basis for the image Im(A). d) Is it true that the linear system Ax = b is consistent for any possible choice of vector b? Does A have full rank? e) If a linear system Ax = b is consistent, what is the dimension of the solution space?
Added by Richard G.
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To find the kernel of A, we need to find the solutions to the homogeneous system Ax = 0. We can do this by row reducing the matrix A to its row echelon form. A = | 1 2 1 | | 2 4 1 | | 1 2 2 | Row reduce A: R2 = R2 - 2*R1 R3 = R3 - R1 A_reduced = | 1 2 Show more…
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