Column Matrix Teacher Resources

In this vector spaces and subspaces learning exercise, students review column spaces of matrices. They determine if the set of all 2 by 2 matrices is a vector space. Students determine if the set of all invertible 2 by 2 matrices is a...

In this fundamental theorem worksheet, student explore the nullspace and column space of given matrices. They explore the vectors needed to make it linearly independent and construct free variable columns. This two-page worksheet...

In this vector space instructional activity, students find the column spaces of given matrices. This two-page instructional activity contains examples, theorems, explanations, and approximately three problems.

In this least squares instructional activity, students solve 3 different problems that include determining the least squares of equations. First, they use the data given in the table to write out the normal equations a system of 2...

In this vector spaces learning exercise, learners identify the vector in a given set.  They explore addition and scalar multiplication in their vectors.  This two-page learning exercise contains 13 problems.

Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...

In this chemistry worksheet, learners calculate the eigenfunction of the operator. They use the operator matrices. There are 4 questions.  

In this algebra worksheet, 9th graders solve a riddle like puzzle involving matrices and linear equations. They have to find the missing numbers in the square, using the given numbers.

Readers of Shakespeare’s Twelfth Night use a magic squares matrix to match vocabulary words from Act II, Scene 5 with their definitions. An answer key is provided.

In this projection worksheet, students determine the projections of a given matrix. This four-page worksheet contains explanations and examples and approximately ten problems to complete.

In this permutations worksheet, students identify a transpose matrix, and create a permutation matrix. This three-page worksheet contains six problems.

In this algebra worksheet, students solve problems with matrices. They add, subtract and multiply matrices. There are 7 questions.

In this vector spaces worksheet, students explore the column and rowspace of a matrix. They find the basis of subspaces associated with a given matrix. Students observe the relationship between vectors and the nullspace. This...

In this Eigenvalue and Eigenvector worksheet, students examine the applications of matrix exponentiation. This four-page worksheet provides explanations and examples, as well as three problems to complete.

In this linear algebra instructional activity, students complete matrix multiplication. They find the row space and nullspace of given matrices. This two-page instructional activity contains examples, explanations, and approximately...

In this linear system worksheet, students explore the characteristics of given matrices. They multiply matrices and determine pivots and multiply solutions. This four-page worksheet contains approximately seven problems.

Students determine the dimension of a subspace.  In this dimension and rank instructional activity, students explore the dimension of a vector space.  They compare and explore the relationship in a matrix. 

In this review of vectors instructional activity, students explore vectors and their uses. They multiply and subtract vectors and identify the linear combinations of given matrices. This two-page instructional activity contains...

In this basis and dimension activity, students explore vector spaces associated with rectangular matrices. The two-page activity contains approximately 20 short answer questions.

In this addition matrix puzzle worksheet, learners insert 8 numbers into the matrix so that the numbers add up vertically, horizontally, and diagonally.

In this addition matrix puzzle, students insert the proper numbers to make the rows, columns, and diagonals add up to the proper numbers.

In this linear algebra worksheet, students examine a matrix, determine the vectors, list the parameters, and identify the null space. Students explain the parameters in the description of the null space There are four problem solving...

What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...

Sal solves a complex determinant problem from the 2010 IIT entrance test. Knowledge of determinants, the exponential form of complex numbers, trigonometric ratios, and algebraic thinking are all utilized here.