Q5 of 75 Page 8

If and are two square matrices, find A B and hence solve the system of linear equations: X – y = 3, 2x + 3y + 4z = 17, y + 2z = 7.

A = B =

AB =


AB =


Now, we can see that it is AB = 6I. where I is the unit Matrix


Or, A – 1 =


Now the given equation can be written as:



A X B


Or, X = A – 1B


=



=


X =


Hence, x = 2,y = – 1 and z = 4


More from this chapter

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4

Show that each one of the following systems of linear equations is inconsistent

3x – y – 2z = 2


2y – z = – 1


3x – 5y = 3

 4

Show that each one of the following systems of linear equations is inconsistent

x + y – 2z = 5


x – 2y + z = – 2


– 2x + y + z = 4

 6

If , find A – 1 and hence solve the system of linear equations:2 x – 3 y + 5z = 11, 3x + 2y – 4z = – 5, x + y – 2z = – 3

 7

Find A – 1, if . Hence, solve the following system of linear equations:

x + 2y + 5z = 10, x – y – z = – 2,


2x + 3y – z = – 11