Linear Algebra is Harder than Calculus: Why It’s the Case

An Overview of Linear Algebra

Linear algebra is a branch of mathematics dealing with comprehensive systems of linear equations and linear inequalities, as well as matrices. Linear algebra is often taught in high school and college because it is a core component of calculus. Some people say that linear algebra is harder than calculus but others disagree with this statement. One way to think about this is that linear algebra is a very extensive topic which covers many different systems that deal with linear equations and inequalities. If you’ve taken your first year of calculus, then you have had the opportunity to study linear algebra at some point in the semester and if you look back in your notes, there is some discussion on linear systems. However, if you were to look at the entirety of the course, there would be a lot more topics that provide a strong background for linear algebra.
A linear system is composed of an equation and some variables. An equation is a set of values and variables are the numbers you can use to represent these values. For example, let’s say that we take the equation \(\sin(x)=y \). The variable \(x\) can represent the number 0, and an infinite number of numbers in between. Now let’s say that we have input a value of 0 which produces an output of 1 but if we input 10, then the output will be -1. The variable \(y\) is used to represent this number 1. The equation \((\sin(x)=y) \) has a solution (output) of 1. If we have 2 equations, then there are infinitely many solutions and the output of each solution is also represented by a number.
Some Basic Concepts

is linear algebra harder than calculus
is linear algebra harder than calculus

Linear Algebra – A Quick Overview

Linear algebra is a branch of mathematics dealing with comprehensive systems of linear equations and linear inequalities. Linear algebra covers many different systems. Some systems include linear algebraic functions and relations. Linear algebra covers many different systems. Linear algebra is often taught in high school and college because it is a core component of calculus. Some people say that linear algebra is harder than calculus but others disagree with this statement. One way to think about this is that linear algebra is a very extensive topic which covers many different systems that deal with linear equations and inequalities. This can make it seem complicated but it is not as hard as many people believe. Here is an abstract that goes over the different aspects of linear algebra. Linear algebra encompasses a large range of topics, including polynomials and rational functions, quadratic and cubic equations with solutions of high degree, functions in one variable, matrices, determinants, eigenvalues and eigenvectors, square roots and other transcendental functions.
Linear Algebra Properties
The following table lists several properties of linear algebraic systems. The first column lists the property while the second column provides a definition of the property.
PROPERTY DEFINITION
Linearity With respect to addition, if formula_1 are row vectors and formula_2 is a scalar then:
Summation (sigma) With respect to addition, if formula_3 is a row vector then:
Additive identity 0 is the additive identity for the operation of addition.
Multiplicative identity 1 is the multiplicative identity for the operation of multiplication.
Associativity An identity (i.e., equality) of the form formula_4 is equivalent to another identity of the form formula_5.
Distributivity The following identities are equivalent:

is linear algebra harder than calculus
is linear algebra harder than calculus