CLASS NOTES ON LINEAR ALGEBRA 1. Matrices Suppose that F is
... 1. Ψ gives a 1-1 correspondence between n × n matrices and bilinear forms on F n . 2. Ψ gives a 1-1 correspondence between n × n symmetric matrices and symmetric forms on F n 3. Ψ gives a 1-1 correspondence between invertible n × n symmetric matrices and nondegenerate symmetric forms From now on in ...
... 1. Ψ gives a 1-1 correspondence between n × n matrices and bilinear forms on F n . 2. Ψ gives a 1-1 correspondence between n × n symmetric matrices and symmetric forms on F n 3. Ψ gives a 1-1 correspondence between invertible n × n symmetric matrices and nondegenerate symmetric forms From now on in ...
FinalExamReviewMultC..
... • D. The set S could be either linearly dependent or linearly independent, depending on the case. • E. The set S is linearly independent, as long as no vector in S is a scalar multiple of another vector in the set. • F. none of the above Solution: (Instructor solution preview: show the student solut ...
... • D. The set S could be either linearly dependent or linearly independent, depending on the case. • E. The set S is linearly independent, as long as no vector in S is a scalar multiple of another vector in the set. • F. none of the above Solution: (Instructor solution preview: show the student solut ...
ch7
... Matrix Form of the Linear System (1). (continued) We assume that the coefficients ajk are not all zero, so that A is not a zero matrix. Note that x has n components, whereas b has m components. The matrix a1n b1 a11 ...
... Matrix Form of the Linear System (1). (continued) We assume that the coefficients ajk are not all zero, so that A is not a zero matrix. Note that x has n components, whereas b has m components. The matrix a1n b1 a11 ...
