1 7 mark 1 3 -1 . Let A = | -2 -6 5 and let B be the row-reduced echelon form of A. Find the first 3 9-3 row of matrix B. A: [1 0 0 B: [1 3 - 1] C: [1 3 2] D: (1 3 0 E: [1 0 3]

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johnjehu68Lv6

15 Jan 2023

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4. (12 points) Let the matrix A and its reduced row echelon form R be given by the following. A= [ 1 -2 2 -3 1 -2 4 -1 4 1 -3] [1001 1] -4 0 0 1 0 1 1 7 -1 0 0 1 1 -1 | = R. (a) Find a basis for the column space of A. (b) Find a basis for the row space of A. (c) Find a basis for the null space of A. (d) Verify that the dimension of the column space of A plus the dimension of the null space of A is equal to the number of columns of A.

(10] 1. Given that /1 0 2 1 -1 2 0 3 0 1 A4 07 2-1 0 0 1 3 1 / has reduced row echelon form R= (1 000 17 0 0 1 0 -11 0001 4: OOOOO find a basis for each of the following: (a) The row space of A. (b) The column space of A. (c) The null space of A.

mark 18. Consider the linear system Ax = b where A is a 5 x 5 invertible matrix. Which one of the following statements is false? A: There is a row of five zeroes in the row-reduced echelon form of A. | B: The rank of A is 5. C: The rank of Ab] is 5. D: The system Ax = b has a unique solution. E: The system Ax = 0 has only the trivial solution.

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1 7 mark 1 3 -1 . Let A = | -2 -6 5 and let B be the row-reduced echelon form of A. Find the first 3 9-3 row of matrix B. A: [1 0 0 B: [1 3 - 1] C: [1 3 2] D: (1 3 0 E: [1 0 3]

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