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Linear Algebra II: Matrix Algebra

This course takes you through roughly three weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology.

...
Linear Algebra II: Matrix Algebra

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6,052 already enrolled!
Starts Mar 22
Ends May 14
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Starts May 15
Ends Aug 13
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Starts Aug 21
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Starts Jan 8, 2024
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Linear Algebra II: Matrix Algebra

This course takes you through roughly three weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology.

Linear Algebra II: Matrix Algebra
3 weeks
5–6 hours per week
Self-paced
Progress at your own speed
Free
Optional upgrade available

Choose your session:

6,052 already enrolled! After a course session ends, it will be archivedOpens in a new tab.
Starts Mar 22
Ends May 14
Enroll
Starts May 15
Ends Aug 13
Enroll
Starts Aug 21
Enroll
Starts Jan 8, 2024
Enroll
Linear Algebra II: Matrix Algebra

About this course

Skip About this course

Your ability to apply the concepts that we introduced in our previous course is enhanced when you can perform algebraic operations with matrices. At the start of this class, you will see how we can apply the Invertible Matrix Theorem to describe how a square matrix might be used to solve linear equations. This theorem is a fundamental role in linear algebra, as it synthesizes many of the concepts introduced in the first course into one succinct concept.

You will then explore theorems and algorithms that will allow you to apply linear algebra in ways that involve two or more matrices. You will examine partitioned matrices and matrix factorizations, which appear in most modern uses of linear algebra. You will also explore two applications of matrix algebra, to economics and to computer graphics.

Students taking this class are encouraged to first complete the first course in this series, linear equations.

At a glance

  • Institution: GTx
  • Subject: Math
  • Level: Intermediate
  • Prerequisites:
    None

What you'll learn

Skip What you'll learn

Upon completion of this course, learners will be able to:

  • Apply matrix algebra, the matrix transpose, and the zero and identity matrices, to solve and analyze matrix equations.
  • Apply the formal definition of an inverse, and its algebraic properties, to solve and analyze linear systems.
  • Characterize the invertibility of a matrix using the Invertible Matrix Theorem.
  • Apply partitioned matrices to solve problems regarding matrix invertibility and matrix multiplication.
  • Compute an LU factorization of a matrix and apply the LU factorization to solve systems of equations.
  • Apply matrix algebra and inverses to solve and analyze Leontif Input-Output problems.
  • Construct transformation matrices to represent composite transforms in 2D and 3D using homogeneous coordinates.
  • Construct a basis for a subspace.
  • Calculate the coordinates of a vector in a given basis.
  • Characterize a matrix using the concepts of rank, column space, and null space.
  • Apply the Rank, Basis, and Matrix Invertibility theorems to describe matrices, subspaces, and systems.

About the instructors

Ways to take this course

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Verified Track
Audit Track

Price

$199 USD

Free

Access to course materials

Unlimited

Limited

Expires on Apr 12

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Shareable certificate upon completion

Graded assignments and exams

Read our FAQsin a new tab about frequently asked questions on these tracks.

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