Matrices, Vector Spaces and Subspaces 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.

... 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 ...

... 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 ...

... where ( 9) (pr(u) = orthogonal projection of vector "u" onto ... and (dot product of two orthogonal vectors is null ... Using the simple echelon form of matrix, we will ...

... Find a basis B of R^n such that the B-matrix B of ... to zero v) The 3×3 matrices A such that vector [1; 2 ... is in the kernel of A vi) The 3×3 matrices in reduced ...

... Linear Algebra Matrices (VIII) Eigen Values, Eigen Vectors, Eigen ... Then is an eigen vector corresponding to the eigen value ... as three columns of a matrix, we get ...

... 2. Find the orthogonal projection of the vector u = (-2, 2, 3 ... dependent since the determinant of the matrix is zero ... of the space spanned by the vectors given is 2 ...

... Consider a permutation matrix such that , then has non-zero ... ring.) Let V be an n- dimensional vector space over K ... EndK(V), the ring of n × n matrices over K ...

Linear Transformations, Matrices, Orthogonal Projections. ... v. If we set a matrix. ... So we can define a column vector T ( ) C = c1 c2 L cp (3.14). So: yP = AC (3.15). ...

... complete a proof regarding subspaces of finite dimensional vector space. 1) Consider the given vectors as row matrices. Write down the echlon matrix whose rows ...