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

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Discussion Overview

The discussion revolves around solving a set of equations involving the inverses of matrices A, B, and C. The focus is on deriving expressions for the variable X in various matrix equations, with an emphasis on the implications of matrix multiplication properties.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Some participants propose methods for solving the equations by manipulating the equations using the inverses of the matrices.
  • One participant suggests that for equation (a), multiplying both sides by A⁻¹ leads to X = A⁻¹C.
  • Another participant indicates that for equation (b), applying A⁻¹ on the left and B⁻¹ on the right yields X = A⁻¹CB⁻¹.
  • For equation (c), a participant claims X = (C + B)A⁻¹B⁻¹.
  • In addressing equation (d), one participant states X = B⁻¹C⁻¹D, while another emphasizes the importance of the order in matrix multiplication.
  • Participants remind each other that matrix multiplication is not commutative, which affects the order of operations in their solutions.

Areas of Agreement / Disagreement

There is no consensus on the final forms of the solutions for equations (c) and (d), as participants present different approaches and expressions. The discussion remains unresolved regarding the correctness of the proposed solutions.

Contextual Notes

Participants have not explicitly stated all assumptions or provided detailed justifications for their steps, which may affect the validity of the solutions. The dependence on the properties of matrix multiplication is a critical aspect of the discussion.

fazal
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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...
 
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fazal said:
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?
 
so
c) X=(C+B)A^-1B^-1

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

plse check thks
 
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
 
Last edited:

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