Published on 31 Jan 2019

School

Department

Course

Professor

MT Q S

İ S. Y

M ,

Surname, Name:

Q . §. M O

Let A=

1−1

2 2

1 0

and B=[3 1

−4 4 ]. Is there a matrix Csuch that

CA =B?

A

Let us say C=[x1x2x3

x4x5x6]so that CA =B. Then we get

[x1x2x3

x4x5x6]

1−1

2 2

1 0

=[3 1

−4 4 ]

[x1+ 2x2+x3−x1+ 2x2

x4+ 2x5+x6−x4+ 2x5]=[3 1

−4 4 ].

In other words, we obtain the following system

x1+ 2x2+x3= 3

−x1+ 2x2= 1

x4+ 2x5+x6=−4

−x4+ 2x5= 4

We have the augmented matrix

121000 3

−120000 1

000121−4

000120 4

∼

1−20000−1

0 00120 4

0 00001−8

0 00000 0

Since we have a solution for the system above, we conclude that there exists

a matrix Csuch that CA =B.

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