Write as a Matrix Worksheets
How to Write Linear Systems as a Linear Matrix?
Equations are mathematical statements that include constants, variables, arithmetic operations, with an equals-to sign. There are different forms of the equation, and the most basic form is the linear equations. These equations have a variable with the highest power 1. The general form of a linear equation is given by;
ax + by = c
Here a, b, and c are constants, and x, y are variables. When there is a system of linear equations, we can also write it in the form of a linear matrix. What is a matrix? Well, a matrix is an arrangement of numbers in a rectangular form; it comprises of rows and columns. A linear matrix is one which represents a system of linear equations So, how to write linear systems as a linear matrix? Consider a linear system;
To create a linear matrix, you need to create a co-efficient matrix, a variable matrix, and a constant matrix. A co-efficient matrix comprises of all the co-efficient of the variables. In this case, it becomes;
Now, the variable matrix can be written as; (x/y) The constant matrix is written as; (c/f) The system can now be written as;
When you apply matrix multiplication here; it will become;
Guides students through writing linear equations as matrices. Step 1: Write the coefficients of x in the first column of first matrix. Step 2: Write the coefficients of y in the second column of first matrix. Step 3: Write x, y in the second matrix column wise. Step 4: Write the equivalent of the equations in the third matrix putting a "=" sign in between them.View worksheet
Which British mathematician gave his name to a sort of algebra used in computing?
Answer: George Boole, the inventor of Boolean algebra.