Column Matrix Teacher Resources

There are four fundamental theorems of mathematics: arithmetic, algebra, calculus, and linear algebra listed here. Each one is described on this poster or handout. The challenge for a student of math is to figure out why they are...

Let the lab be a catalyst to learn about enzymes. Scholars create alginate beads filled with yeast. As part of an investigation into enzymes, they see how these beads provide a catalyst to the reaction of glucose into ethanol.

In this ecology community status worksheet, students research their state's ecosystem, make a chart of the biodiversity, analyze the chart and identify issues with wetland species.  This page has several links to helpful web resources.

Students differentiate the types of cryptosystems and use them to communicate privately. In this algebra lesson, students use substitution and transposition to identify the cryptographs. They send and receive cryptograms as they try...

In this food web relationships worksheet, students click on the links to learn about the food web relationships in the wetlands and answer short answer questions about it. Students complete 8 questions total.

Students develop an understanding of pi and the relationship between the diameter, radius and circumference. After a lecture/demo, students use construction paper and a compass to solve problems using diameter, radius and circumference.

Eleventh graders define various types of linear systems and three types of solutions. In this linear system and echelon forms lesson, 11th graders solve a linear system using elementary row operations. Students also describe the set of...

Eleventh graders study homogeneous linear systems. In this linear system of equations lesson, 11th graders write linear system solutions in parametric vector form. Students also identify the connection between linear independence and...

Students define vocabulary related to vectors and investigate vector problems. In this math instructional activity, students define basis and explore plotting vectors in correlation to their basis. Plotting polynomials facilitates...

Third graders explore the elements of a story using fairy tales from all over the world. They compare and contrast story elements, key ideas and concepts found in a variety of texts from around the world.

Video first gives examples of finding the column space and null space of a matrix. Shows how to determine if the column space is a basis. Gives an example of finding the basis of the column space if the column space is not already a...

Video starts with reviewing matrix notation. Defines multiplying a matrix by a vector and shows examples. Shows how the matrix-vector products can be interpreted as the dot product of column vectors with a matrix or as a weighted linear...

Video reviews how to find a basis for the column space and talks about how to find it more efficiently using reduced row echelon form. Shows a visualization of the column space in R3 as a plane. Shows two methods to determine the...

Video defines the column space as a linear combination of the column vectors and relates it to span. Shows that the column space is a valid subspace. Shows several ways to interpret a column space. This video also appears in the strand...

Video first reviews what the null space is and how to solve for it using reduced row echelon form. Shows that any solution to the inhomogeneous system Ax = b will be the sum of a particular solution and a homogeneous solution. Extends...

Video shows how to find the basis and dimension of the column space by finding its reduced row echelon form and using the columns corresponding to the pivot columns as the basis. Explains that rank is the dimension of the column space....

Video demonstrates how to calculate the null space of a matrix by creating a system of equations and using reduced row echelon form to solve and represent the null space by a linear combination of vectors and by the span of vectors. This...

Video defining an orthogonal matrix as a square matrix C whose columns form an orthonormal set. Shows that C will be invertible and that multiplying C transpose by C will result in the identity matrix. The result that C transpose equals...

Video explaining that the transpose of a matrix is created by switching rows and columns. The idea is shown abstractly and specifically with 2x2 matrix and 4x3 matrix. Also shows that the transpose of a transpose is the original matrix....

Video first introduces the identity matrix and shows that when any vector is multiplied by the identity matrix the result is the original vector. Also shows that the columns of the identity matrix are called the standard basis for R^n....

Video first introduces the identity matrix and shows that when any vector is multiplied by the identity matrix the result is the original vector. Also shows that the columns of the identity matrix are called the standard basis for R^n....

Video first reviews the criteria for a subspace and then goes through the steps to show the null space meets the criteria and is a a subspace. This video also appears in the strand Algebra: Matrices. [10:21]

Examples, solutions, videos, and lessons to help students learn how to multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of...

This video models clearly how to multiply a row vector, which is equivalent to a one-column matrix, by a matrix. It explains that the dimension of the resultant matrix will have the number of rows of the first matrix and the number of...