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Unformatted text preview: pr.4 (15 pts.) Let A be a 7 by 9 matrix with rank 4. Find (a) The number of pivot variables (b) The number of free variables (c) How many solutions does the system of equations Ax = have? (d) dim( N ( A T )) = pr.5 (10 pts.) Let A be a 3x2 matrix with rank 2. (a) How many pivots does A have? (b) Let R be the reduced echelon form of A . Which columns of R are the pivot columns? (c) Which rows of R are the pivot rows? (d) What are the values of the pivots of R ? (e) What are the values of the elements of R which are not pivots? (f) Write down the matrix R . pr.6 (20 pts.) Find the complete solution (also called general solution) to 12 3 1 37 11 3 49 14 4 x 1 x 2 x 3 x 4 = 4 14 18...
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 Spring '08
 Johnson,G
 Math, Linear Algebra, Algebra

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