Solving Equations Involving A⁻¹, B⁻¹ and C⁻¹

[fazal]

Given that A^-1 , B^-1 and C^-1 exist, solve the following equations for X:

a)AX=C
b)AXB=C
c)BXA=C+B
d)XABC=D

plse help...

 

[HallsofIvy]

Given that A^-1 , B^-1 and C^-1 exist, solve the following equations for X:

a)AX=C
b)AXB=C
c)BXA=C+B
d)XABC=D

plse help...

a) Multiply both sides of the equation on the left by A^-1:
A^-1AX= X= A^-1C.
b) Multiply both sides of the equation on the left by A^-1 and on the right by B^-1:
A^-1AXBB^-1= X= A^-1CB^-1

Can you try c and d now?

 

[fazal]

so
c) X=(C+B)A^-1B^-1

d)X=B^-1C^-1D

plse check thks

 

[NoMoreExams]

c)BXA=C+B

Therefore XA = B^(-1)(C+B) therefore X = B^(-1)(C+B)A^(-1)

Remember matrix multiplication is NOT commutative.

Do the same steps for d), note ORDER MATTERS