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Perplex
Perplex
Dashboard
Topics
Exponents & LogarithmsApproximations & ErrorSequences & SeriesMatricesComplex NumbersFinancial Mathematics
Cartesian plane & linesFunction TheoryModellingTransformations & asymptotes
2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random VariablesInference & Hypotheses
DifferentiationIntegrationDifferential Equations
Review VideosFormula BookletMy Progress
BlogLanding Page
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Perplex

Matrices (Lesson 1/5)

Foundations of Matrices

1 / 27

Discussion

The following table shows the voting preferences of ​4​ voters in an election with ​3​ candidates.


Candidate A

Candidate B

Candidate C

Albert

​1st​

​2nd​

​3rd​

Britney

​1st​

​2nd​

​3rd​

Chaz

​3rd​

​1st​

​2nd​

Denise

​3rd​

​2nd​

​1st​

(a)

Fill in the following table for the number of ​1st,  ​2nd​ and ​3rd​ votes received by each candidate.


​1st​

​2nd​

​3rd​

Candidate A




Candidate B




Candidate C




Solution:

Look down each voter’s row and tally how often each candidate appears in 1st, 2nd, and 3rd.

  • Candidate A: 1st by Albert and Britney → 2 firsts; never 2nd → 0 seconds; 3rd by Chaz and Denise → 2 thirds

  • Candidate B: 1st by Chaz → 1 first; 2nd by Albert, Britney, Denise → 3 seconds; never 3rd → 0 thirds

  • Candidate C: 1st by Denise → 1 first; 2nd by Chaz → 1 second; 3rd by Albert and Britney → 2 thirds


​1st​

​2nd​

​3rd​

Candidate A

2

0

2

Candidate B

1

3

0

Candidate C

1

1

2

Matrices (Lesson 1/5)

Foundations of Matrices

1 / 27

Discussion

The following table shows the voting preferences of ​4​ voters in an election with ​3​ candidates.


Candidate A

Candidate B

Candidate C

Albert

​1st​

​2nd​

​3rd​

Britney

​1st​

​2nd​

​3rd​

Chaz

​3rd​

​1st​

​2nd​

Denise

​3rd​

​2nd​

​1st​

(a)

Fill in the following table for the number of ​1st,  ​2nd​ and ​3rd​ votes received by each candidate.


​1st​

​2nd​

​3rd​

Candidate A




Candidate B




Candidate C




Solution:

Look down each voter’s row and tally how often each candidate appears in 1st, 2nd, and 3rd.

  • Candidate A: 1st by Albert and Britney → 2 firsts; never 2nd → 0 seconds; 3rd by Chaz and Denise → 2 thirds

  • Candidate B: 1st by Chaz → 1 first; 2nd by Albert, Britney, Denise → 3 seconds; never 3rd → 0 thirds

  • Candidate C: 1st by Denise → 1 first; 2nd by Chaz → 1 second; 3rd by Albert and Britney → 2 thirds


​1st​

​2nd​

​3rd​

Candidate A

2

0

2

Candidate B

1

3

0

Candidate C

1

1

2