© 2017 Yves Nievergelt Homework on Inverse Complex Matrices Due Tuesday 10Octobe

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© 2017 Yves Nievergelt Homework on Inverse Complex Matrices Due Tuesday 10October 2017, I (0 point) PLEASE WRITE YOUR NAME SOMEWHERE ABOVE HERE! Books, notes, calculators, computers, and cell phones are allowed but you must still show each step. Help from other people is allowed but you must still give them credit. Please show all your work for consideration for partial credit. Check your solutions; ifa check fails, then state so. For this homework set, you may use any available resource, for instance, calculators, computers, discussions with anyone, libraries, and web sites. However, you must write and submit your own final solutions. Problem 1 (10 points) Calculate the inverse matrix, A-1, if any exists, of the matrix A = | 31-1 4+1-3-1 Optionally check all your results with any computing system. Note any discrepancy, if any arises.

Explanation / Answer

Write the augmented matrix

Make the pivot in the 1st column by dividing the 1st row by 1+i

Multiply the 1st row by -1+3i

Subtract the 1st row from the 2nd row and restore it

Multiply the 1st row by -1+5i

Subtract the 1st row from the 3rd row and restore it

Find the pivot in the 2nd column in the 2nd row

Multiply the 2nd row by (1-i)/(1+i)

Subtract the 2nd row from the 1st row and restore it

Multiply the 2nd row by 4i/(1+i)

Subtract the 2nd row from the 3rd row and restore it

Make the pivot in the 3rd column by dividing the 3rd row by -4i/(1+i)

Multiply the 3rd row by (-1+i)/(1+i)

Subtract the 3rd row from the 1st row and restore it

There is the inverse matrix on the right

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Result:

A1 A2 A3 B1 B2 B3 1 1+i 1-i -1+i 1 0 0 2 -1+3i 4+i -3-i 0 1 0 3 -1+5i 7+3i -7-3i 0 0 1

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