Systems of equations with Matrices | IB Math AIHL | Perplex

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Topics

Exponents & Logarithms Approximations & Error Sequences & Series Matrices Complex Numbers Financial Mathematics

Cartesian plane & lines Function Theory Modelling Transformations & asymptotes

2D & 3D Geometry Voronoi Diagrams Trig equations & identities Vectors Graph Theory

Probability Descriptive Statistics Bivariate Statistics Distributions & Random Variables Inference & Hypotheses

Differentiation Integration Differential Equations

Review Videos Formula Booklet My Progress

Blog Landing Page

Matrices (Lesson 4/5)

Systems of equations with Matrices

1 / 11

Discussion

Consider the system of equations

{ax+2y=33x+3y=4

Let x=(xy), and b=(34).

(a)

Write the system of equations in the form Ax=b, where A is a matrix.

Solution:

Think of each equation as a “row” of numbers multiplying (xy). Put the x- and y-coefficients into a matrix so that multiplying recreates the left-hand sides.

AAx=(a323)=(a323)(xy)=(34)

So the system is Ax=b with A=(a323).

Matrices (Lesson 4/5)

Systems of equations with Matrices

1 / 11

Discussion

Consider the system of equations

{ax+2y=33x+3y=4

Let x=(xy), and b=(34).

(a)

Write the system of equations in the form Ax=b, where A is a matrix.

Solution:

Think of each equation as a “row” of numbers multiplying (xy). Put the x- and y-coefficients into a matrix so that multiplying recreates the left-hand sides.

AAx=(a323)=(a323)(xy)=(34)

So the system is Ax=b with A=(a323).