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  3. 4 consider the matrix 1001 1 a1 1 1 0...

Question: 4 consider the matrix 1001 1 a1 1 1 0...

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4. Consider the matrix 1001 1 A-1 1 1 0 2-1 | and the vector b- 19 Summer Session MATHS 208 - Assignment 2 Page 1 of2 (a) Construct the augmented matrix [A]b and use elementary row operations to trans- form it to reduced row echelon form. (b) Find a basis for the column space of A (c) Express the vectors v4 and vs, which are column vectors of column 4 and 5 of A, as linear combinations of the vectors in the basis found in (b) (d) Find a basis for the null space of A (e) Find a particular solution to the linear system Ax -b (f) Find the general solution to the linear system Ax -b (g) Can you find a vector c such that Ax-c has no solution? Give your reason 14 marks)

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