John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 6, 2023
Calculus

Creating Unit Vectors: How to Normalize a Given Vector for Same Direction

Find unit vector (u) with the same direction To find a unit vector with the same direction as a given vector, we need to normalize the given...

John Rhodes
July 6, 2023
Calculus

Understanding Vector AB: How to Calculate and Represent Displacement

Given the points A(x1,y1) and B(x1,y1) the vector a with representation AB is The vector AB is the displacement vector that represents the direction and magnitude needed...

John Rhodes
July 6, 2023
Calculus

Understanding the Equation of a Sphere: Derivation and Calculation of Radius

Equation of a Sphere with Center (h,k,l) and radius r The equation of a sphere with center (h, k, l) and radius r can be written as:...

John Rhodes
July 6, 2023
Calculus

The Distance Formula in Three Dimensions: Calculating the Distance Between Points in a 3D Coordinate System

Distance Formula in 3 Dimensions The distance formula in three dimensions is used to find the distance between two points in a 3D coordinate system The distance...

John Rhodes
July 6, 2023
Linear Algebra

Is the Row Space of the Transpose of a Matrix the Same as the Column Space of the Original Matrix? A Proof.

A denotes an m×n matrix. Determine whether the statement is true or false. Justify your answer.The row space of AT is the same as the column space...

John Rhodes
July 6, 2023
Linear Algebra

The Range of a Linear Transformation: A Vector Space Proof

Determine whether the statement is true or false. Justify your answer.The range of a linear transformation is a vector space. The statement is true The statement is...

John Rhodes
July 6, 2023
Linear Algebra

Understanding and Differentiating the Column Space of a Matrix A and the Solutions of Ax = b

A denotes an m×n matrix. Determine whether the statement is true or false. Justify your answer:The column space of A, Col A, is the set of all...

John Rhodes
July 6, 2023
Linear Algebra

Understanding the Null Space: Proving it as a Vector Space

A denotes an m×n matrix. Determine whether the statement is true or false. Justify your answer: A null space is a vector space. The statement is true...