Linear Systems: Definition of the Nullspace
In this nullspace learning exercise, students find the nullspace of matrices, write a rectangular matrix upper-triangular form, and convert augmented matrix to echelon form. This six-page learning exercise contains approximately 8 problems.
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Solving General Systems of Linear Equations
Examine the usefulness of matrices when solving linear systems of higher dimensions. The lesson asks learners to write and solve systems of linear equations in four and five variables. Using matrices, pupils solve the systems and apply...
11th - 12th Math CCSS: Designed
New Review Inverse Matrices, Column Space and Null Space | Essence of Linear Algebra, Chapter 6
Determine the geometric representation to the solution of a system of linear equations. The resource shows how scholars can represent a system of linear equations as a linear transformation. The video discusses using an inverse matrix to...
12 mins 11th - Higher Ed Math CCSS: Adaptable
New Review Linear Combinations, Span, and Basis Vectors | Essence of Linear Algebra, Chapter 2
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...
10 mins 11th - Higher Ed Math CCSS: Adaptable
Topic 4: Solving Systems of Linear Equations
Linear equations, coordinate planes, and systems of equations are covered in this extremely well-organized instructional activity. Composed of a series of mini-lessons, the instruction aims at explaining a different facet of solving...
8th - 11th Math CCSS: Adaptable