Q&A for How to Understand the Basics of Matrices

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You could calculate it with cofactors, or you could remember the Rule of Alternating Signs: The first element is positive, second is negative, third positive et cetera.

A scalar matrix is a square matrix that is a multiple of the identity matrix. In other words, the values on the main diagonal are all the same number, and every other value not on the main diagonal is zero.

To understand what matrices are, you first have to understand what systems of equations are. Systems of equations are multiple equations with multiple variables like x and y, and when you solve them, you get the intersection between all the equations. Matrices are just another way to represent the systems of equations by using just the coefficients of your equations, that is, the numbers that are before your variables. For example: x+y = 2 3x+5y =7 can be represented as: |1 1 2| |3 5 7|

It's another way to solve a systems of equations. It can be useful when having to solve many variables.