Question

Is the matrix

6 0

0 5
a linear combination of the matrices

1 0

0 1
and

1 0

0 0
?

how do you figure this out?

Answer 1

then
a|1 0|
|0 1|
+
b|1 0|
|0 0|
=
|6 0|
|0 5|

hope this lines up ....

so
|a 0|
|0 a|
+
|b 0|
|0 0 |
=
|6 0|
|0 5|

only true if:
a+b = 6
a+0+5

a = 5 , b = 1 makes it true

yes, it can be expressed as a linear combination