Question #298068

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.



1
Expert's answer
2022-02-15T17:50:21-0500

1.


B(XI)A+B=AB(X-I)A+B=A

B1B(XI)A+B1B=B1AB^{-1}B(X-I)A+B^{-1}B=B^{-1}A

XAA+I=B1AXA-A+I=B^{-1}A

XAA1AA1+IA1=B1AA1XAA^{-1}-AA^{-1}+IA^{-1}=B^{-1}AA^{-1}

XI+A1=B1X-I+A^{-1}=B^{-1}

X=A1+B1+IX=-A^{-1}+B^{-1}+I

5. X=A1+B1+IX=-A^{-1}+B^{-1}+I


2.

3. The system is inconsistent.




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