In a matrix equation, the unknown is a matrix.

**A · X = B**

To solve, check that the matrix is invertible, if it is, premultiply (multiply to the left) both sides by the matrix inverse of A.

If the equation is of type **X · A = B**, the members must postmultiply (multiply to the right) because matrix multiplication is not commutative.

1. Given the matrices . Solve the equation: A** ·** X = B

|A|=1 ≠ 0, there is the inverse A^{-1 } .

A^{-1} (A ** ·** X) = A^{-1} ** ·** B

(A^{-1} ** ·** A) ** ·** X = A^{-1} ** · **B

I ** ·** X = A^{-1} ** · **B

X = A^{-1} ** · **B

2. Given the matrices . Solve the equation: X** ·** A + B = C

|A| = 1 ≠ 0

(X ** ·** A + B) − B = C − B

X ** ·** A + (B − B) = C − B

X ** ·** A + 0 = C − B

X ** ·** A = C − B

X · A · A^{-1} = (C − B) · A^{-1}

X (A · A^{-1} ) = (C − B) · A^{-1}

X · I = (C − B) · A^{-1}

X = (C − B) · A^{-1}

3.Solve the matrix equation:

**A · X + 2 · B = 3 · C**

**|A| = 1 ≠ 0**

**(A · X +2 · B) − 2 · B = 3 · C − 2B**

**A · X + ( 2 · B − 2 · B) = 3 · C − 2B**

**A · X + 0= 3 · C − 2B**

**A · X = 3 · C − 2B**

(**A ^{−1} · A) · X = A^{−1} · (3 · C − 2B)**

**I · X = A ^{−1} · (3 · C − 2B)**

**X = A ^{−1} · (3 · C − 2B)**

4.Solve the matrix equation:

To solve a system of linear equations, it can be transformed into a matrix equation and then solved.

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