Linear Algebra Help with Exercise 4 Thanks Let A 3 x y 4 B

Linear Algebra Help with (Exercise 4) Thanks

Let A = [3 x y 4], B = [z 3 4 -1] C = [-1 6 4 14], and D = [-3 9 15 -1]. Find x, y, and z, if possible, so that 3A - 2B = C AB = C AB = D BA - D + C = [2 7 2 3].

Solution

a) 3A - 2B = C

3A = [ 9 3x

3y 12 ]

2B = [ 2z 6

8 -2]

3A - 2B = [ 9 -2z 3x- 6

8-3y 14]

C = [-1 6

4 14 ]

9 -2z =-1

-2z = -10

z =5

3x -6 = 6

x =4

8 -3y =4

3y =4

y =4/3

b) AB = C

[ 3z +3x 9-x

yz +16 3y -4]

9 -x =6

x =15

3y -4 = 14

y =6

yz +16 =4

yz = -12

6y =-12

y =-2

c) AB = D

[ 3z +3x 9-x

yz +16 3y -4]

9 -x =9

x =18

3y-4 = -1

3y =3

y =1

yz +16 =15

yz =1

1z =1

z =1

d)BA -D +C

BA = [ 3z +3y xz+12

12-y 4x -4 ]

BA - D =[ 3z+3y +3 xz +12 -9

12-y -15 4x-4 +1]

BA - D +C =

[ 3z+3y + 2 xz +9

-y +1 4x-3 +14]

[ 3z+3y +2 xz+9

-y+1 4x +11]

now 4x+11 = 3

4x=-8

x =-2

-y+1 =2

-y = 1

y =-1

xz +9 =7

xz =-2

-2z =-2

z =1