State the Rank-Nullity Theorem. Let A = -3 1 2 -4 12 6 0 3 -9 -4 -2 (i) Find bases for row (A), col(A) and N(A). (ii) Determine the rank and nullity of A, and verify that the Rank-Nullity Theorem holds for the above matrix A.

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A: Step 1: Step 2: Step 3:

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Q: Find (a) a basis for the row space and (b) the rank of the matrix.

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Q: (b) Find a matrix P which diagonalizes the matrix A = 101 010 101

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Q: = 1 -2 2 00 0 -1 0 0 -1

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Q: Consider the following matrix: A = N 4 Ń 1 2 -1 023

A: Basis for null space and row space of A and rank -nullity of A

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A: Solve the following