Expert: Paul Klarreich - 11/27/2008

Question
1.find the determinant of the following 5x5 matrix

4 1 8 2 5
1 0 0 3 1
4 2 3 1 3
6 4 4 1 0
7 3 1 2 2

i have trued using the row reducing method such that i could get a triangular matrix so that i could simply add multiply the major row but i got zero

2.solve the following systems of equations using the row echelon method
W+2X-Y+4Z=7
W+3Y+2Z=10
2W+6X+Y-5Z=8
3W-3X+2Y+Z=4
PLEASE SHOW ALL THE WORKING THANK YOU VERY MUCH."


Answer
Questioner:   RONALD
Category:  Advanced Math
Private:  No
 
Subject:  maths
Question:  1.find the determinant of the following 5x5 matrix

4 1 8 2 5
1 0 0 3 1
4 2 3 1 3
6 4 4 1 0
7 3 1 2 2

I have tried using the row reducing method such that I could get a triangular matrix so that I could simply add multiply the major row but I got zero.

>> And how did you know it was wrong?


Anyway, it is -- you can check your calculations at:

http://www.bluebit.gr/matrix-calculator/calculate.aspx


2.solve the following systems of equations using the row echelon method

W+2X-Y+4Z=7
W+3Y+2Z=10
2W+6X+Y-5Z=8
3W-3X+2Y+Z=4

Write the 'augmented' matrix:

1   2   -1   4   7
1   0    3   2   10
2   6   1   -5   8
3  -3   2    1   4

Now use the row-reducing methods described above.  Eventually you get:

1 ................
0  1 ...............
0  0   1 .........
0  0   0  1 ......

And the last row means  Z = constant, which you can now back substitute.

I'll leave that work to you.  That site will do the work, too.