How to Simplify a Matrix Equation?

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In summary, the given equations are two matrices and they are equal if and only if their corresponding entries are equal. By simplifying the equations, it is found that z = 2x and t = -y.
  • #1
helpm3pl3ase
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x+2y y+2t = 5x -y

4x+3z 4y+3t = 5z -tIam just not sure how they simplified these equations to this:

z = 2x, t = -y??

Please help.
 
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  • #2
helpm3pl3ase said:
x+2y y+2t = 5x -y

4x+3z 4y+3t = 5z -t


Iam just not sure how they simplified these equations to this:

z = 2x, t = -y??

Please help.
Your notation is confusing. You have a blank in the first equation between 2y and y. Similarly in the second equation between 3z and 4y. What do you mean??
 
  • #3
The two are separate matrices

Like one is
x+2y y+2t
4x+3z 4y+3t

And the other is
5x -y
5z -t

And they set them equal and simplify to

z = 2x, t = -y

I don't get how they got that?
 
  • #4
You have a 4x4 matrix on the left.

What is on the right?
 
  • #5
I have no 4x4

one matrix is 2x2:

(First column)
x+2y
4x+3z
(Second Column)
y+2t
4y+3t

Second matrix is 2x2:

(First column)
5x
5z
(Second Column)
-y
-t
 
Last edited:
  • #6
helpm3pl3ase said:
x+2y y+2t = 5x -y

4x+3z 4y+3t = 5z -t


Iam just not sure how they simplified these equations to this:

z = 2x, t = -y??

Please help.
Now that we have it clear that these are matrices, they must give, since two matrices are equal if and only if their corresponding entries are equal,
x+2y= 5x, y+ 2t= -y, 4x+ 3z= 5z, and 4y+ 3t= -t.
The third equation is just 4x= 2z (subtract 3z from both sides). Also, the fourth equation is the same as 4y= -4t (subtract 3t from both sides) so t= -y as claimed.
 
  • #7
Ahh I understand now... Thank you so much for the help.
 

1. How can I simplify a matrix equation?

To simplify a matrix equation, you can use various algebraic operations like addition, subtraction, multiplication, and division. You can also use properties of matrices, such as the associative and distributive properties, to simplify the equation.

2. What is the purpose of simplifying a matrix equation?

The purpose of simplifying a matrix equation is to make it easier to solve and understand. Simplifying can also help to identify patterns and relationships within the matrix equation.

3. Can I use row operations to simplify a matrix equation?

Yes, row operations can be used to simplify a matrix equation. These operations include multiplying a row by a scalar, swapping rows, and adding a multiple of one row to another.

4. Are there any special rules for simplifying a matrix equation?

Yes, there are some special rules for simplifying a matrix equation. For example, the order of operations is important, just like in regular algebra. Also, when multiplying matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

5. Is it possible to simplify a matrix equation with variables?

Yes, you can simplify a matrix equation with variables just like you would with regular algebra. You can use the same operations and rules to simplify the equation, but the final solution may include variables instead of specific numbers.

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