Answer to Question #298068 in Linear Algebra for Pheeha

Question

1.Solve for X from the matrix equation below. Here l is the identity matrix and det(B) ≠ 0 and det(A) ≠ 0.

B(X - l)A + B = A

Choose the correct option:

1. No such matrix X.

2. X=A–¹ B - A.

3. X=A–¹ - B +A.

4. X=A–¹ + B -A.

5. X= -A–¹ + B–¹ + l.

6. X= -(A–¹ + B–¹).

2. Consider the following linear system:

2x - 3y = -1

2x - 3y = 1

1. x=0 and y= 0 satisfy the system.

2. The system has exactly one solution.

3. The system is inconsistent.

4. The system has infinitely many solution.

Answer 1

1.

$$B(X-I)A+B=A$$

$$B^{-1}B(X-I)A+B^{-1}B=B^{-1}A$$

$$XA-A+I=B^{-1}A$$

$$XAA^{-1}-AA^{-1}+IA^{-1}=B^{-1}AA^{-1}$$

$$X-I+A^{-1}=B^{-1}$$

$$X=-A^{-1}+B^{-1}+I$$

5. $X=-A^{-1}+B^{-1}+I$

2.

3. The system is inconsistent.