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  • John Rhodes
  • June 21, 2023
  • Linear Algebra

Translating The Solution Set Of Homogeneous Systems: The Role Of Particular Solutions

translating the solution set of Ax = 0, using any particular solution p of Ax = b for the translation Theorem 6 says that if Ax =...
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  • 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...
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  • 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,...
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  • 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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