Y – z, when y = –4 and z = –3 find the value

Answer [ 4,3 x 5 ] =[y z 1 5 ]

As the given matrices are equal, their corresponding elements are also equal.
Comparing the corresponding elements, we get: x=1,y=4, and z=3
[ x+ y 2
5 + z xy ] = [ 6,2 , 5,8 ]

As the given matrices are equal, their corresponding elements are also equal. Comparing the corresponding elements, we get:

x+y=6,xy=8,5+z=5

Now, 5+z=5⇒z=0

We know that:
(x−y)
2
=(x+y)
2
−4xy
⇒(x−y)
2
=36−32=4
⇒x−y=±2

Now, when x−y=2 and x+y=6, we get x=4 and y=2
When x−y=−2 and x+y=6, we get x=2 and y=4
∴x=4,y=2 and z=0orx=2,y=4 and z=0
[ x+ y +z
X+z
Y+z ] = 9,5,7

As the two matrices are equal, their corresponding elements are also equal. Comparing the corresponding elements, we get:

x+y+z=9 (1)
x+z=5 (2)
y+z=7 (3)

From (1) and (2), we have:
y+5=9
⇒y=4

Then, from (3), we have: 4+z=7
⇒z=3
∴x+z=5
⇒x=2
∴x=2,y=4 and z=3