MAM1012S 2021 Short test 3. Includes 2 Questions on Gauss Jordan Reduction. PDF

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Summary

This short test focusses on work covering Gauss Jordan Reduction. Be very careful when doing these questions, as its very easy to make silly mistakes. Accurate sub calculations are crucial to success in this test. Make sure to follow exact format!...

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UNIVERSITY OF CAPE TOWN Department of Mathematics and Applied Mathematics MAM1012S 2021 Short Test 3

Total marks: 15

Instructions: 1. 2. 3. 4.

Write your name and student number clearly at the top of the first page of your script. Follow this by writing the statement: ‘These answers are entirely my unassisted work’ Sign your name. When you have finished the test, scan your script to pdf format, upload this to the Assignments Tool on the Vula MAM1012S site before the cut-off time of 18:00 Monday 30 August.

Show ALL working and reasons 1. Use Gauss-Jordan reduction to solve the system of simultaneous equations:

[7]

 − =1 2 +  = 4 −+=4 2. In solving a system of four equations in four unknowns: , , , and , James arrived at the following stage in his Gauss-Jordan reduction: x 1 0 0 0

y 0 1 0 0

z 1 -2 1 2

w 2 -3 2 4

3 0 -1 -2

[5]

Complete the reduction process.

3. On checking his working, James discovered he had made a mistake and instead of what he had, as shown in question 2, he should have arrived at x 1 0 0 0

y 0 1 0 0

z 1 -2 1 2

w 2 -3 2 4

Complete his reduction process using this corrected stage.

3 0 -1 2

[3]...