Setting up a matrix from a linear equation

In summary, setting up a matrix from two linear equations involves rewriting the equations in standard form and then using the coefficients to fill in the matrix. To solve the equations, matrix multiplication can be used by ensuring that the number of columns of the first matrix is equal to the number of rows of the second matrix.
  • #1
Llewelyn
2
1

Homework Statement


I need some help with a question on my assignment. It asks to set up a matrix from the linear equations, y=25x+70 and y=35x+40.

Homework Equations


How do I set this matrix up?

The Attempt at a Solution


I think that I have to rewrite it as 25x-y=-70 and 35x-y=-40. But then I am stuck. How do you set up the matrix?
 
Physics news on Phys.org
  • #2
Do you know how to do matrix multiplication? Write out:

##\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} e \\ f \end{bmatrix}##

and fill in ##a, b, c, d, e, f##.
 
  • #3
Thank you
 
  • #4
Llewelyn said:
Thank you
No metion please, you can extend the same method for solving simultaneous equations with more number of variables provided that the number of equations available is same as the number of unknown variables. [emoji4]
 
  • #5
Dick said:
Do you know how to do matrix multiplication? Write out:

##\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} e \\ f \end{bmatrix}##

and fill in ##a, b, c, d, e, f##.
Make sure that the number of rows of first matrix is equal to the number of columns of the second matrix that are multiplied
Then multiply the corresponding elements of row of matrix_1 with that of elements of columns of matrix_2 and add them together.
Do the same with the available columns of matrix_2
Do the same for all the rows and columns and you will get the matrix with its order as( no. of columns of matrix_1 * no. of rows of matrix_2)
Hope that helps
 
  • #6
jishnu said:
Make sure that the number of rows of first matrix is equal to the number of columns of the second matrix
No, this is incorrect. For matrix multiplication to be defined, the number of columns of the first matrix has to equal the number of rows in the second matrix. For example, if A is 3x2 (i.e., 3 rows and 2 columns) and B is 2x4, the resulting product matrix will be 3x4.

If A were 2x3 (2 rows and 3 columns), and B were 4x2 we have the number of rows of the first matrix (A) being equal to the number of columns of the second matrix (B as you said, but the multiplication is not conformable (not defined).
 
  • #7
Mark44 said:
No, this is incorrect. For matrix multiplication to be defined, the number of columns of the first matrix has to equal the number of rows in the second matrix. For example, if A is 3x2 (i.e., 3 rows and 2 columns) and B is 2x4, the resulting product matrix will be 3x4.

If A were 2x3 (2 rows and 3 columns), and B were 4x2 we have the number of rows of the first matrix (A) being equal to the number of columns of the second matrix (B as you said, but the multiplication is not conformable (not defined).
Yeah, this is the correct way which I actually tried to express but got messed up with the row and column and unknowingly was interchanged, I apologize for the same
 

Related to Setting up a matrix from a linear equation

1. How do I set up a matrix from a linear equation?

To set up a matrix from a linear equation, we first need to identify the coefficients of the variables in the equation. These coefficients will become the entries in our matrix. The constants in the equation will become the entries in the last column of the matrix.

2. What is the purpose of setting up a matrix from a linear equation?

Setting up a matrix from a linear equation allows us to use matrix operations to solve the equation. This can be useful in solving systems of equations or finding the inverse of a matrix.

3. Can I set up a matrix from any linear equation?

Yes, you can set up a matrix from any linear equation, as long as it has two or more variables. The number of equations should also match the number of variables in order to have a unique solution.

4. How do I identify the variables in a linear equation to set up a matrix?

The variables in a linear equation are typically represented by letters such as x, y, or z. They are the unknown values that we are trying to solve for. In a matrix, each variable will have its own column and each equation will have its own row.

5. Are there any shortcuts or tricks to setting up a matrix from a linear equation?

There are a few shortcuts that can make setting up a matrix from a linear equation easier. For example, you can use the augmented matrix method where the coefficients and constants are combined into one matrix. Additionally, you can use technology such as calculators or computer programs to set up the matrix for you.

Similar threads

  • Precalculus Mathematics Homework Help
2
Replies
57
Views
3K
  • Precalculus Mathematics Homework Help
Replies
1
Views
803
  • Precalculus Mathematics Homework Help
Replies
25
Views
1K
  • Precalculus Mathematics Homework Help
Replies
32
Views
927
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Precalculus Mathematics Homework Help
Replies
6
Views
561
  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
  • Precalculus Mathematics Homework Help
Replies
8
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
837
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
Back
Top