Mathematics | Senioritis

John Rhodes
June 21, 2023
Linear Algebra

Row Echelon Form: What A Row Of Zeros In The Matrix Means For Solving Systems Of Equations

HW 3: If the REF of the augmented matrix of a consistent equation Ax = b has a row of zeros, then the equation has infinitely many...

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John Rhodes
June 21, 2023
Linear Algebra

Proven: Infinitely Many Solutions In A Consistent Matrix Equation Ax=B Leads To Ref With A Row Of Zeros

HW 3: If a consistent equation Ax = b, where A is a square matrix, has infinitely many solutions, then the REF of the augmented matrix has...

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John Rhodes
June 21, 2023
Linear Algebra

Proving Linear Independence Of {V1, V2, V3, V4, V1+V4} Using Equations

HW 4: If the set {v1, v2, v3, v4} is linearly independent, then {v1, v2, v3, v4, v1+v4} is linearly independent. FALSE. The vector v1+v4 is a...

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John Rhodes
June 21, 2023
Linear Algebra

Linear Dependence: Proving Relationships Between Vectors

HW 4: If a set of vectors is linearly dependent then at least one of the vectors is a scalar multiple of another one. FALSE. Consider the...

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John Rhodes
June 21, 2023
Linear Algebra

Counterexample Disproves The Claim That All Sets Of Three Vectors In R2 Are Linearly Dependent

HW 4: A set of 3 vectors in R 2 is always linearly dependent. TRUE. When row reducing A = [v1 v2 v3], where v1, v2, v3...

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John Rhodes
June 21, 2023
Linear Algebra

Proving Linear Dependency: The Relationship Between Z And Span{X, Y}.

HW 4: If {x, y} is linearly independent, and if z is in Span{x, y}, then {x, y, z} is linearly dependent. TRUE. Since z is in...

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John Rhodes
June 21, 2023
Linear Algebra

Proving The Statement: If A System Has Infinitely Many Solutions, The Matrix Isn’T Invertible.

HW 5: Let A be an n × n matrix, and b be a vector in R^n . If the system Ax = b has infinitely many...

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John Rhodes
June 21, 2023
Linear Algebra

How To Prove That If Ab = Ac And A Is An Invertible Square Matrix, B = C

HW 5: Let A be an invertible square matrix. If AB = AC, then B = C. TRUE. AB = AC–> A^−1 (AB) = A^−1 (AC) –>...

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