question archive Consider all 3 x 3 matrices such that the sum of each row and each column is the same
Consider all 3 x 3 matrices such that the sum of each row and each column is the same
Subject:MathPrice: Bought3
Consider all 3 x 3 matrices such that the sum of each row and each column is the same. One can show that the set of all such matrices is a subspace of the space of all 3 x 3 matrices (with the usual matrix addition and multiplication by a scalar). Let V denote this subspace. You are also given that V = span { Pi, P2, Pa, PA, P5, Pa} with 0 1 P1= 1 , 12 = 0 , Pa = 1 0 0) 0 0) 0 0) 0 10 0 PA 1 P's = 0 0 P6 = 0 0 (a) (5 pts) Write down the equation to solve in order to check the linear independence (or not) of the above six matrices /'1, ..., /'s as vectors in V. (b) (3 pts) Solve the equation in your answer to part (a) above. Are the six matrices above linearly independent?
Consider the following two bases of 12, the vector space of polynomials with degree at most two and real
coefficients: B = (1, 21, -2 + 412), C = {1,1-t,2-4t +12 ]. (a) (4 pts) Compute directly s, c. (b) (4 pts) Compute
the change of basis matrix C / B. (c) (2 pts) Check your calculations above by verifying that c = (C PB) [B.
