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a 1
Show(prove) that the set of all 2 X 2 matrices of the form with addition defined by
1 b

a 1 c 1 a+c 1
+ =
...

Solution Summary

Matrices, Vector Spaces and Zero Vectors are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

... It is not a vector space, since V is NOT closed under finite scalar multiplication. For instance, take a 2 by 2 matrix with integer entries. ... b) all matrices ab. ...

...Vector Spaces, Linear Transformations, and Eigenvalues / Eigenvectors ... Basis and Diagonalizing Matrices are investigated ... 2 an eigenvalue of the following matrix? ...

... 8) We have to check now the 3x3 matrices. ... by the vectors containing the non-singular matrix of above ... 12) The dimension of the corresponding vector space will be ...

... is in W. (b) If k is any scalar and u is any vector in W ... Let V be the set of all 2 x 2 matrices with integer ... if we use a real number k to multiply a matrix A in ...

Subspaces of the Vector Space of 2-by-2 Matrices. Need help with this homework problem. ... Infinite thanks! 10. Let A be a particular vector in R^2x2. ...

Vector Spaces : Rank. ... 0] [ 4 0 3 0] [ 5 0 -1 0] : is a 4 x 4 matrices [ 2 -3 ... Rank of a matrix is equal to the number of linearly independent rows in the matrix...

Algebra: vector space. ... 1,2) element is 0. c)The subset of matrices of the form ( ab ) (-bc ) d)The subset of 2x2 matrices whose determinants are zero. ...

... diagonal elements are not equal to 1. The set of all 2×2 matrices of the ... With the standard matrix addition and scalar multiplication. This is a vector space. ...

... For each of the following vector spaces V, we wish to give its ... a) The set of all symmetric matrices. Every symmetric matrix can be written in the following form ...