Matrix Algebra

 Sometimes, there’s a need to work with multiple numbers at one time. Typically, these numbers will be arranged into a matrix. It’s important to understand matrix algebra to understand how the matrices work and to be able to do operations with them.

What’s Inside a Matrix?

A matrix includes a grid of numbers, called an array. These numbers are arranged in rows or columns. The way in which the numbers are organized is called its dimensions. The dimensions are typically written as 3 by 5 or 2 by 7 where the first number is the number of rows in the array and the second number is the number of columns. For example, in a 2 by 7, there are 2 rows and 7 columns of numbers.

Determining if Matrices are Equivalent

Matrices are equivalent if they have the same number of rows, the same number of columns, and the elements are equal. The elements are the numbers or symbols in the rows and columns of a matrix. For example, if A and B are both 2 by 3 matrices, and they both have the same numbers in the same order, they are equivalent. If B has an x instead of one of the numbers, but it’s known they’re equivalent, the student can look through A to find out what x is supposed to be.

Matrix Operations – Adding and Subtracting Matrices

It is possible to add and subtract matrices, but only if they have the same number of rows and columns. If they do, the corresponding elements can be added or subtracted. For example, A has 2 rows and 2 columns. If B has 2 rows and 2 columns, it is possible to add or subtract A and B. Only add or subtract the corresponding elements with each other and be careful to keep them in the correct order to get the correct answer. If A needs to be subtracted from B, the subtraction done will be a B element minus an A element for each element in the array.

Multiplying a Matrix

It’s possible to multiply a matrix by a number. In this case, it’s important to ensure the numbers stay in the proper position inside the matrix. Matrix A has 2 rows and 2 columns. The numbers in the array are, for row 1, 3 and 4, and for row 2, 4 and 6. Multiply this by 2 to get matrix B. To do this, multiply each number by 2 and place the new number in the corresponding space of the new matrix. With this example, matrix B would have 6 and 8 in row 1 and 8 and 12 for row 2.

It’s also possible to multiply 2 matrices. When they have the same number of rows and columns, it works similarly to adding or subtracting. It’s important to pay close attention to the order of the elements when multiplying to get the numbers in the right positions.

Matrices often look complicated because of the number of elements in them. Being careful to pay attention to the order of the elements can make it easy to add, subtract, or multiply two matrices together to get the final answer and to work with multiple numbers at one time.