Sophia Learning
Sophia: Row Operations: Lesson 8
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 8 of 9 in the series titled "Row Operations."
Sophia Learning
Sophia: Row Operations: Lesson 9
This lesson introduces the basic row operations that can be performed on matrices, explaining why they are valid things to do and providing examples of each. It is 9 of 9 in the series titled "Row Operations."
Sophia Learning
Sophia: Sarrus' Rule: Lesson 5
This lesson introduces Sarrus' rule. It is 5 of 6 in the series titled "Sarrus' Rule."
Sophia Learning
Sophia: Sarrus' Rule: Lesson 1
This lesson introduces Sarrus' rule. It is 1 of 6 in the series titled "Sarrus' Rule."
Sophia Learning
Sophia: Scalar Multiplication: Lesson 2
This lesson will introduce scalars, and demonstrate how to perform scalar multiplication with matrices. It is 2 of 10 in the series titled "Scalar Multiplication." [3:01]
Sophia Learning
Sophia: Singular and Non Singular Matrices: Lesson 4
This lesson introduces the notion of a singular matrix and provides a shortcut to determine whether or not a given 2x2 matrix is singular. It is 4 of 5 in the series titled "Singular and Non-Singular Matrices."
Sophia Learning
Sophia: Singular and Non Singular Matrices: Lesson 5
This lesson introduces the notion of a singular matrix and provides a shortcut to determine whether or not a given 2x2 matrix is singular. It is 5 of 5 in the series titled "Singular and Non-Singular Matrices."
Sophia Learning
Sophia: Using Determinants to Classify 2x2 Matrices
This lesson demonstrates how the determinant of a 2x2 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.
Sophia Learning
Sophia: Using Determinants to Classify Systems of 3x3 Matrices
This lesson demonstrates how the determinant of a 3x3 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.
Sophia Learning
Sophia: Using Matrices to Organize Data: Lesson 3
This lesson provides real-world examples that demonstrate how to organize data into matrices. It is 3 of 5 in the series titled "Using Matrices to Organize Data." [4:43]
Sophia Learning
Sophia: Using Matrices to Organize Data: Lesson 5
This lesson provides real-world examples that demonstrate how to organize data into matrices. It is 5 of 5 in the series titled "Using Matrices to Organize Data." [2:51]
Sophia Learning
Sophia: Vectors and Tensors: Lesson 3
In this lesson, students are introduced to vectors and tensors, and their significance when working with matrices. Students should be familiar with the concept of a matrix before beginning this lesson. It is 3 of 4 in the series titled...
Sophia Learning
Sophia: Verifying That Matrices Are Inverses: Lesson 3
This lesson demonstrates how to determine whether or not matrices are inverse. It is 3 of 7 in the series titled "Verifying that Matrices are Inverses."
Sophia Learning
Sophia: Verifying That Matrices Are Inverses: Lesson 7
This lesson demonstrates how to determine whether or not matrices are inverse. It is 7 of 7 in the series titled "Verifying that Matrices are Inverses."
Sophia Learning
Sophia: Verifying That Matrices Are Inverses: Lesson 1
This lesson demonstrates how to determine whether or not matrices are inverse. It is 1 of 7 in the series titled "Verifying that Matrices are Inverses."
Sophia Learning
Sophia: Zero Determinant: Lesson 3
This lesson goes over matrices with a determinant of zero. It is 3 of 7 in the series titled "Zero Determinant." [2:14]
Sophia Learning
Sophia: Zero Determinant: Lesson 4
This lesson goes over matrices with a determinant of zero. It is 4 of 7 in the series titled "Zero Determinant." [2:44]
Sophia Learning
Sophia: Zero Determinant: Lesson 5
This lesson goes over matrices with a determinant of zero. It is 5 of 7 in the series titled "Zero Determinant." [2:47]
Sophia Learning
Sophia: Dot Products
This lesson introduces the concept of a dot product and its relationship to matrix operations.
Sophia Learning
Sophia: Equality in Matrices
This lesson discusses when two matrices are considered equal. This is part of a series of lessons on early concepts related to matrices.
Sophia Learning
Sophia: Matrix Addition and Subtraction
This lesson explains how to add and subtract matrices when it is possible to do so, noting matrix addition is commutative and associative. [2:59]
Sophia Learning
Sophia: Equality in Matrices: Lesson 3
This lesson discusses when two matrices are considered equal. This is part of a series of lessons on early concepts related to matrices. It is 3 of 4 in the series titled "Equality in Matrices."
Sophia Learning
Sophia: Matrix Multiplication
This lesson introduces matrix multiplication, distinguishes it from multiplying by a scalar, and provides examples of the operation.
Sophia Learning
Sophia: Matrix Multiplication: Lesson 2
This lesson introduces matrix multiplication, distinguishes it from multiplying by a scalar, and provides examples of the operation. It is 2 of 2 in the series titled "Matrix Multiplication."