Matrix Equations: Solving for X using Inverse and Transpose

Published on June 2, 2025

Linear-Algebra

Solve matrix equations to find the unknown matrix X using matrix inverse and transpose properties.

Question

Answer

The problem asks us to solve for the matrix

in three different matrix equations using matrix properties.

denotes the

identity matrix.

Part a)
The given equation is

.
First, let’s find the transpose of the matrix on the right side:

So the equation becomes:

Let

. We have

.
Taking the inverse of both sides:

Now we need to find the inverse of

. For a

matrix

, its inverse is

.
For

, the determinant is

.
So,

Now substitute

back into the equation:

We know

Subtract

from both sides:

Finally, multiply by

Part b)
The given equation is

.
Let

. We have

.
Taking the inverse of both sides:

Now we need to find the inverse of

. For

, the determinant is

.
So,

Now substitute

back into the equation:

We know

Subtract

from both sides:

Finally, multiply by

Part c)
The given equation is

.
First, let’s find the transpose of the matrix on the right side:

So the equation becomes:

Let

and

.
The equation is

.
To solve for

, we need to multiply by

on the right side:

Then, multiply by

Now we need to find the inverse of

. For

, the determinant is

.
So,

Now calculate

Finally, multiply by

The final answer is

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features

Matrix Equations: Solving for X using Inverse and Transpose

Question

Answer

Related math solutions

Débloquez la version web à vie

Related math solutions