Exercise 1

Given the matrices:

Solve the matrix equation:

A · X = B

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Exercise 2

Given the matrices:

Solve the matrix equation:

X · A + B = C

Exercise 3

Given the matrices:

Solve the matrix equations:

Exercise 4

Given the matrices:

Solve the matrix equation:

A X + 2 B = 3 C

Exercise 5

Solve the matrix equation:

A · X + 2 · B = 3 · C

Exercise 6

Solve the system using a matrix equation.

Exercise 7

Calculate A and B:

Exercise 8

Solve the following equations without developing the determinants.

1

2

Solution of exercise 1

1Given the matrices:

Solve the matrix 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

Solution of exercise 2

Given the matrices:

Solve the matrix 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

Solution of exercise 3

Given the matrices:

Solve the matrix equations:

Solution of exercise 4

Given the matrices:

Solve the matrix equation:

Solution of exercise 5

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)

Solution of exercise 6

Solve the system using a matrix equation.

Solution of exercise 7

Calculate A and B:

Multiply the second equation by −2.

Add the equations.

Multiply the first equation by 3 and add the equations:

Solution of exercise 8

Solve the following equations without developing the determinants.

1

2

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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