Question

Write the given system in the matrix form?

Answer 1

To convert a system of equations to matrix form, form three matrices: A for coefficients, X for variables, and B for constants, then write the equation as A*X = B. For the example given, the matrix form is [2 3; 4 -6][x; y] = [5; -2].

Step-by-step explanation:

To write a system of equations in matrix form, you need to arrange the coefficients of the variables along with the constants into a matrix equation A*X = B. Consider the following system of equations as an example:

• 2x + 3y = 5
• 4x - 6y = -2

First, identify the coefficients of the variables for each equation. In matrix form, the coefficients will form matrix A, the variables will form matrix X, and the constants will form matrix B.

Matrix A (the coefficients matrix) will be:

• 2 3
• 4 -6

Matrix X (the variables matrix) will be:

• x
• y

Matrix B (the constants matrix) will be:

• 5
• -2

Now, the matrix equation A*X = B represents:

• [2 3] * [x] = [5]
• [4 -6] [y] [-2]

This is the matrix form of the system of equations given.