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  • John Rhodes
  • July 8, 2023
  • Linear Algebra

Understanding Matrix Multiplication and Dimensions: Explaining why C, the product of matrices A and B, has the same number of columns as A and the same number of rows as B.

Suppose A, B, and C are matrices, and C = AB is defined. Then C has the same number of columns as A and the same number...
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  • John Rhodes
  • July 8, 2023
  • Linear Algebra

Investigating the Properties of Matrix Multiplication: False Statement, Matrix AB = 0

If A and B are matrices, and the product AB is the zero matrix, then A or B must be a zero matrix. To determine if the...
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  • John Rhodes
  • July 8, 2023
  • Linear Algebra

Proving C = D: All Corresponding Entries in C and D are Equal

If B, C, D, are square n x n invertible matrices and BC = BD, then C = D. To prove that C = D, we need...
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  • John Rhodes
  • July 8, 2023
  • Linear Algebra

Proving that if AB = 0, then either A or B is a zero matrix

If AB = 0, then either A or B is a zero matrix. To prove that if AB = 0, then either A or B is a...
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  • John Rhodes
  • July 8, 2023
  • Linear Algebra

The Relationship Between Coincident Lines and Infinitely Many Solutions in a System of Linear Equations

In a system of two linear equations, if two linear equations have the same graph, then the associated system has infinitely many solutions. In a system of...
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  • John Rhodes
  • July 8, 2023
  • Linear Algebra

A Guide to Understanding Solutions of Systems of Linear Equations

A system of linear equations either has no solutions, one solution, or infinitely many solutions. That’s correct! A system of linear equations is a set of two...
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  • John Rhodes
  • July 8, 2023
  • Linear Algebra

Proving x – 2y = 0 when x is twice y: Step-by-Step Explanation with Examples

If quantity x is twice quantity y, then x − 2y = 0. To prove that x – 2y = 0 when x is twice y, we...
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  • John Rhodes
  • July 8, 2023
  • Linear Algebra

Does a Row Reduced Matrix Always Have a 1 in the Second Column of the Second Row? Exploring Different Scenarios

A row reduced matrix always has a 1 in the second column of the second row. A row reduced matrix is achieved by applying a sequence of...
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