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These are the notes of Exam of Linear Algebra which includes Initial Value Problem, General Solution, Erential Equation, Origin Parallel, Line, Vector Space, Dimension etc. Key important points are: Inverse, Compute the Inverse, Skew Symmetric, Invertible, Odd Positive Integer, Solutions, System, Rule, Volume, Linear Transformations
Typology: Exams
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Specify whether the matrix has an inverse without trying to compute the inverse
(a) An n × n matrix A is called skew-symmetric if At^ = −A. Show that if A is skew-symmetric and n is an odd positive integer, then A is not invertible.
(b) Let A =
1 λ 0 1 1 1 0 0 1
. Determine those values of λ for which A is invertible.
Find all solutions to the system using Cramer’s Rule.
x 1 − 2 x 2 − 2 x 3 = 3 −x 1 + 2 x 2 + 3 x 3 = 1 2 x 1 − 2 x 2 − 2 x 3 = − 2
Find the inverse of the matrix below using the inverse formula
