General Knowledge Review topics. For the general knowledge, I\'ll be asking some
ID: 3110321 • Letter: G
Question
General Knowledge Review topics. For the general knowledge, I'll be asking some questions about some of the concepts of linear algebra we've seen. They won't be in-depth calculations but rather testing how well you can answer questions regarding these concepts. For example, I could ask: "This matrix A has determinant 0. What does this tell you about the solutions to Ax = b?" or "If det(A) = 0, what does this tell you about the diagonalizability of A?" There may also be some simple calculation questions with some of these concepts. How row reduction works and solutions to linear systems of equations. Matrices, matrix multiplication, and algebra of matrices. Determinants, properties of determinants, and uses of determinants. Vector spaces and their properties, including spans, linear independence, and bases. Linear transformations: definition and examples of. Eigenvalues, eigenvectors, and diagonalization.Explanation / Answer
If detA=0, then rank(A)<n.
Then if rank(A|B)=n then then the system Ax=B has no solution.
If rank(A|B)<n and rank(A|B)=rank (A) then system has infinitely many solutions.
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