Matrix Help

D

Daitcher

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Sep 13, 2022
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I literally dont even know where to start. Any and all help is very much welcome!
 
You have to try something

1st column a b c
2nd column d e f
3rd column g h i
4th column j k l

a + b + c = 1
d + e + f = 1
g + h + i = 1
j + k + l = 1

a + b = c, d + e = f, g + h = i, j + k + l

All I did was what they told me to do.

The question is can you find A, B and C?

Did you post the entire problem?
 
Yes that is the entire problem, here is the solution as well, I just don't know how to get there...Screenshot_20220913_210906.jpg
 
Steven G said:
You have to try something

1st column a b c
2nd column d e f
3rd column g h i
4th column j k l

a + b + c = 1
d + e + f = 1
g + h + i = 1
j + k + l = 1

a + b = c, d + e = f, g + h = i, j + k + l

All I did was what they told me to do.

The question is can you find A, B and C?

Did you post the entire problem?
Click to expand...
Ooops, Băd mistake above
Where I wrote rows, I should have written column.
 
Daitcher said:
View attachment 34035
I literally dont even know where to start. Any and all help is very much welcome!
Click to expand...
Picture the matrix A. What column matrix could you multiply it by on the right to get a column matrix whose entries are the sums of the entries in each row of A? If A satisfies the first condition, this product will be all 1's.

Now, what (different) column matrix could you multiply A by on the right to do something related to the second condition?

Then put them together. You'll have a matrix B such that AB will equal your C when A satisfies the conditions.

Give it a try, so we can see what more help you need.
 
Steven G said:
Ooops, Băd mistake above
Where I wrote rows, I should have written column.
Click to expand...
But you did not write "rows" anywhere in that post!!! See below

Steven G said:
1st column a b c
2nd column d e f
3rd column g h i
4th column j k l

a + b + c = 1
d + e + f = 1
g + h + i = 1
j + k + l = 1

a + b = c, d + e = f, g + h = i, j + k + l

All I did was what they told me to do.

The question is can you find A, B and C?

Did you post the entire problem?
Click to expand...
 
I suggest approaching this from the other end. Can you write down expressions for [imath]y_{11}[/imath] and [imath]y_{12}[/imath] in the following equation ?:

[math]\left( \begin{array}{ccc} x_{11} & x_{12} & x_{13}\\ x_{21} & x_{22} & x_{23}\\ x_{31} & x_{32} & x_{33}\\ x_{41} & x_{42} & x_{43} \end{array}\right) \left( \begin{array}{rr} 1 & 1 \\ 1 & 1 \\ 1 & -1 \end{array}\right) = \left( \begin{array}{cc} y_{11} & y_{12}\\ y_{21} & y_{22}\\ y_{31} & y_{32}\\ y_{41} & y_{42} \end{array}\right)[/math]How about [imath]y_{21}[/imath] and [imath]y_{22}[/imath] ? Get it?
 
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