Thread: Matrices & Systems of Equations:Matrix Algebra

Hello could someone please help me with the following problems, I just couldn't find my way around it. Thanks!

1) Given the following:
A equals
1 2
1 -2

b equals
4
0

c equals
-3
-2


write c as a linear combination of column vectors a_1 & a_2

2) Let A equals

a_11 a_12
a_21 a_22

Show that if d = a_11 a_22 - a_21 a_12 is not equal 0, then
A inverse equals

1/d * ( {a_22 -a_12} {-a_21 a_11} ) ====> {row 1} {row 2}

Originally Posted by googoogaga

Hello could someone please help me with the following problems, I just couldn't find my way around it. Thanks!

1) Given the following:
A equals
1 2
1 -2

b equals
4
0

c equals
-3
-2


write c as a linear combination of column vectors a_1 & a_2

Suppose , then we may write this as a system of linear equations:




which you can now solve for and .

RonL

Originally Posted by googoogaga

2) Let A equals

a_11 a_12
a_21 a_22

Show that if d = a_11 a_22 - a_21 a_12 is not equal 0, then
A inverse equals

1/d * ( {a_22 -a_12} {-a_21 a_11} ) ====> {row 1} {row 2}

This requires that you multiply the matrices:



and:



to show that this is the 2x2 identity matrix

RonL

I still don't get number two. Once multiplying the matrices, then where do I go from there? And what is the 2*2 identity matrice?

Originally Posted by googoogaga

I still don't get number two. Once multiplying the matrices, then where do I go from there? And what is the 2*2 identity matrice?

You need to show that


-Dan