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
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July 8, 2023
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
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July 8, 2023
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
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July 8, 2023
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
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July 8, 2023
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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John Rhodes
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July 8, 2023
Proving the Incorrectness of If quantity x is twice quantity y, then 2x – y = 0 Mathematically
If quantity x is twice quantity y, then 2x − y = 0. To prove that “If quantity x is twice quantity y, then 2x – y...
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John Rhodes
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July 8, 2023
Understanding Matrix Invertibility: How to Calculate the Determinant and Determine if a Matrix is Invertible
1 1 3 3 The given matric is invertible To determine if a matrix is invertible, we need to calculate its determinant To determine if a matrix...
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John Rhodes
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July 8, 2023
The Multiplication of Row Vector and Column Vector: Explaining the 1 × 1 Matrix Result
If defined, a row times a column is always a 1 × 1 matrix. When defining the multiplication of a row vector and a column vector, the...