Forward elimination changes -2x - 3y = 7 -6x - 10y = 22 -2 -3 - -6-10 -2x-3y=7 -ly=1 That step subtracted 21 reverse step adds l21 times row 1 to row 2. The matrix for that reverse step is L= 9- x = b to a triangular Multiply this L times the triangular system In letters, L multiplies Ux = c to give -2 -3 7 -6 -10 22 -2 0 H H X = solves the first one. Find x that solves the second one. x = -2 0 times row 1 from row 2. The - to get 4 = - -2 -3 [131 0 -1 1 X = C: Write down the 2 by 2 triangular systems Lc = b and Ux = c. Check that c = 1
Forward elimination changes -2x - 3y = 7 -6x - 10y = 22 -2 -3 - -6-10 -2x-3y=7 -ly=1 That step subtracted 21 reverse step adds l21 times row 1 to row 2. The matrix for that reverse step is L= 9- x = b to a triangular Multiply this L times the triangular system In letters, L multiplies Ux = c to give -2 -3 7 -6 -10 22 -2 0 H H X = solves the first one. Find x that solves the second one. x = -2 0 times row 1 from row 2. The - to get 4 = - -2 -3 [131 0 -1 1 X = C: Write down the 2 by 2 triangular systems Lc = b and Ux = c. Check that c = 1
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...
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