3. Simultaneous equations with infinitely many solutions.(a) Consider the equations:I+ 2y = 1(3)2x + 4y = 2.i. Show that the RREF of equation 3 isWe therefore have Or + Oy = 0 = 0 = 0. This is a redundantstatement. It gives us no extra information. We can only concludethat there are infinitely many solutions that satisfy r + 2y = 1.%3Dii. Draw the row picture of equation 3. Using this, explain whythere are many soutions.iii. Using the solutions (1,0) and (-1, 1) draw the column pictureof 3.iv. Usually, we set one of the variables equal to a real parameter.Call this parameter t and set r = t. Write the solutions in termsof t.

Given: x+2y=1 and 2x+4y=2 The data in matrix form is 1224xy=12 i.e., AX=B form The augmented matrix…

a) Consider the equations: I+ 2y = 1 (3) 2r + 4y = 2. i. Show that the RREF of equation 3 is 0 0 We therefore have Ox + Oy = 0 = 0 = 0. This is a redundant statement. It gives us no extra information.We can only conclude that there are infinitely many solutions that satisfy r+ 2y = 1. ii. Draw the row picture of equation 3. Using this, explain why there are many soutions. iii. Using the solutions (1,0) and (-1, 1) draw the column picture of 3. iv. Usually, we set one of the variables equal to a real parameter.

a) Consider the equations: I+ 2y = 1 (3) 2r + 4y = 2. i. Show that the RREF of equation 3 is 0 0 We therefore have Ox + Oy = 0 = 0 = 0. This is a redundant statement. It gives us no extra information.We can only conclude that there are infinitely many solutions that satisfy r+ 2y = 1. ii. Draw the row picture of equation 3. Using this, explain why there are many soutions. iii. Using the solutions (1,0) and (-1, 1) draw the column picture of 3. iv. Usually, we set one of the variables equal to a real parameter.

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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Question

3. Simultaneous equations with infinitely many solutions.
(a) Consider the equations:
I+ 2y = 1
(3)
2x + 4y = 2.
i. Show that the RREF of equation 3 is
We therefore have Or + Oy = 0 = 0 = 0. This is a redundant
statement. It gives us no extra information. We can only conclude
that there are infinitely many solutions that satisfy r + 2y = 1.
%3D
ii. Draw the row picture of equation 3. Using this, explain why
there are many soutions.
iii. Using the solutions (1,0) and (-1, 1) draw the column picture
of 3.
iv. Usually, we set one of the variables equal to a real parameter.
Call this parameter t and set r = t. Write the solutions in terms
of t.

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