Linear algebra and its applications: study guide
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.
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algorithm augmented matrix calculations coefficient cofactor expansion command compute coordinate vectors corresponding Counterexample create definition determinant diagonal entries diagonal matrix diagonalizable difference equation echelon form eigenspace eigenvalues eigenvector enter equation Ax Example False formula free variables Gram-Schmidt process HP-48G Note identity matrix inner product Invertible Matrix Invertible Matrix Theorem KEY IDEAS linear algebra linear combination linear system linear transformation linearly independent lower triangular LU factorization MATLAB menu MTH MATR multiple mxn matrix Note for Section number of columns orthogonal matrix orthogonal projection orthonormal permuted pivot columns pivot positions pivot row Power Method problem produce proj quadratic form rank row operations row reduce rref scalar Section 5.3 sequence shows singular value decomposition solution set SOLUTIONS TO EXERCISES solve span stack statement Study Guide Study Tip subspace symmetric matrix tion trajectory trivial solution True vector space write