John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Geometry

The Properties Of A Square: Definition, Examples, And Differences From A Rectangle

Square A rectangle with four congruent sides What is a square? A square is a geometric shape that comprises four straight and equal sides in a plane,...

John Rhodes
June 21, 2023
Linear Algebra

Why Columns Of A Matrix With M Rows And N Columns Can’T Span R^M For M>N?

HW 3: If a matrix has m rows and n columns, with m > n, the columns of the matrix cannot span R^m. TRUE. If A has...

John Rhodes
June 21, 2023
Linear Algebra

Solving Linear Equations With Matrix A: Unique Or Infinite Solutions?

HW 3: A consistent equation Ax = b where A has more columns than rows can have a unique solution. FALSE. If Ax = b is consistent,...

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...

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...

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...

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...

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...