1. (a) Find the rank and nullity of th4e following system of linear equations: x, + 2x, – x, + 4x, = 0 2.x, – x, + 3x, +3x, = 0 4x, +x, +3x, +9x, =0 X, - x, +x, =0 2x, +3x, – x, + 7x, = 0 (b) State...

1.<br>(a) Find the rank and nullity of th4e following system of linear equations:<br>x, + 2x, – x, + 4x, = 0<br>2.x, – x, + 3x, +3x, = 0<br>4x, +x, +3x, +9x, =0<br>X, - x, +x, =0<br>2x, +3x, – x, + 7x, = 0<br>(b) State Dimension Theorem for Matrices. Find the rank and nullity of the following<br>matrix A:<br>1 -3<br>1<br>3<br>6.<br>0 -3<br>A<br>2 -3 -2<br>4<br>4<br>3 -6<br>5<br>-2<br>2 -4 -5<br>

Extracted text: 1. (a) Find the rank and nullity of th4e following system of linear equations: x, + 2x, – x, + 4x, = 0 2.x, – x, + 3x, +3x, = 0 4x, +x, +3x, +9x, =0 X, - x, +x, =0 2x, +3x, – x, + 7x, = 0 (b) State Dimension Theorem for Matrices. Find the rank and nullity of the following matrix A: 1 -3 1 3 6. 0 -3 A 2 -3 -2 4 4 3 -6 5 -2 2 -4 -5

Jun 04, 2022

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1. (a) Find the rank and nullity of th4e following system of linear equations: x, + 2x, – x, + 4x, = 0 2.x, – x, + 3x, +3x, = 0 4x, +x, +3x, +9x, =0 X, - x, +x, =0 2x, +3x, – x, + 7x, = 0 (b) State...

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