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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Forward elimination changes
-2x - 3y = 7
-6x - 10y = 22
-2
-6
-2x - 3y = 7
-ly=1
-3
-10
x = b to a triangular
That step subtracted l21 =
reverse step adds 21 times row 1 to row 2.
The matrix for that reverse step is L=
Multiply this L times the triangular system
In letters, L multiplies Ux= c to give
-2
-3
7
-6 -10 22
-2
0
0
-31
X =
⇒>
41-1
X =
0
solves the first one. Find x that solves the second one. x =
-2
times row 1 from row 2. The
0
=
−1]
to get
X = C:
-2
0 -1
-3 7
9-
Write down the 2 by 2 triangular systems Lc = b and Ux = c. Check that c =
0
4]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58aa71d3-0b09-4db9-8beb-ffcdb8ec454c%2F64d3303e-de89-4565-9811-65d4dbba70d0%2Fn9pf9rc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Forward elimination changes
-2x - 3y = 7
-6x - 10y = 22
-2
-6
-2x - 3y = 7
-ly=1
-3
-10
x = b to a triangular
That step subtracted l21 =
reverse step adds 21 times row 1 to row 2.
The matrix for that reverse step is L=
Multiply this L times the triangular system
In letters, L multiplies Ux= c to give
-2
-3
7
-6 -10 22
-2
0
0
-31
X =
⇒>
41-1
X =
0
solves the first one. Find x that solves the second one. x =
-2
times row 1 from row 2. The
0
=
−1]
to get
X = C:
-2
0 -1
-3 7
9-
Write down the 2 by 2 triangular systems Lc = b and Ux = c. Check that c =
0
4]
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