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  1. Two excellent ones are Steven Roman’s Advanced Linear Algebra [9] and William C. Brown’s A Second Course in Linear Algebra [4]. Concerning the material in these notes, I make no claims of originality. While I have dreamed up many of the items included here, there are many others which are standard linear algebra

  2. MAT 167: Advanced Linear Algebra Final Exam Solutions Problem 1 (15 pts) (a) (5 pts) State the denition of a unitarymatrix and explain the difference between an orthogonal matrix and an unitary matrix. Solution: A unitary matrix is a square matrix of size whose column vectors form an orthonormal basis for . In other words, a matrix is unitary if

  3. Problem (F'03, #9). Consider a 3x3 real symmetric matrix with determinant 6. Assume (1; 2; 3) and (0; 3; ¡2) are eigenvectors with eigenvalues 1 and 2. Give an eigenvector of the form (1; x; y) for some real x; y which is linearly indepen-dent of the two vectors above. What is the eigenvalue of this eigenvector.

  4. Contents. Problems: What is Linear Algebra. Problems: Gaussian Elimination. Problems: Elementary Row Operations. Problems: Solution Sets for Systems of Linear Equations. Problems: Vectors in Space, n-Vectors. Problems: Vector Spaces. Problems: Linear Transformations. Problems: Matrices. Problems: Properties of Matrices. Problems: Inverse Matrix.

  5. Problem Sets with Solutions. MIT OpenCourseWare is a web based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity.

  6. These are rough notes for the Fall 2019 course, compiled January 10, 2023. Copyright Lior Silberman. These notes are available for traditional academic reuse (with attri-bution), and are specifically excluded from the terms of UBC Policy 81.

  7. Solving Ax = b amounts to nding all in Rn which are transformed into vector b in Rm through multiplication by A.

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