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step by step plz Example. For the given matrix below compute both det(A) and det (5.A). 025 A=|1 7 10 01 3
good hand writing plz 11. (8 points) Let T:R + RP be given by the matrix A= [1 2 3] 0 1 2 [036] (a) Find a basis for Ker(T). (b) Find a basis for Im(T).
for (a) plz thank u!!? 14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For each matrix A below,...
4.(5 pts)Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is diagonalizable. Show that it is, in fact, diagonalizable, and find C and D such that C (you may make this as trivial as you wish!) AC = D 5.(5 pts) Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is NOT diagonalizable. Show WHY it is not diagonalizable. 6. (5 pts) Let T:...
Let A be an 3 x 4 matrix, and B an 4 x 3 matrix. Prove: If AB Is, then the columns of B are linearly independent. Let A be an 3 x 4 matrix, and B an 4 x 3 matrix. Prove: If AB Is, then the columns of B are linearly independent.
Let A be a 5 x 3 matrix whose columns are linearly independent. Prove: If B is an invertible 3 x 3 matrix, then the columns of AB are linearly independent. Let A be a 5 x 3 matrix whose columns are linearly independent. Prove: If B is an invertible 3 x 3 matrix, then the columns of AB are linearly independent.
#4 plz 3. Let F(x, y, z) = (2xyz + sin x)i + x²zj + x²yk. Find a function f such that F = Vf. 4. Evaluate F.ds, where c(t) = (cost, sint, 4), 0 <t<t, and F is as in Exercise 3.
2. Let A be an n x n real symmetric matrix or a complex normal matrix. Prove that tr(A) = X1 + ... + and tr(AⓇA) = 1212 + ... +14.12 where ....... An are the eigenvalues of A repeated with multiplicity (for example, if n = 3 and the eigenvalues of A are -3 and 7 but -3 has multiplicity 2 then 11 = -3, 12 = -3, and Az = 7). 3. Let A be an n x...
)-( 1 (c) Let C be a real 3 x 3 matrix and b be a real 3-vector. The general solution to the matrix equation Cx=b is given by 2 2 =X3 + -4 2 for all XER Let 10 y = -6 8 (i) Let z be a real 3-vector. Find the solution set to the matrix equation Cz=0 (ii) Calculate M1, M2 ER such that 2 y = M1 ( 3 + H2 ·()--() 1 (iii) Express Cy...
linear algebra Let V (71, 72, 3}, where 71 73=(2,0,3). (1,3,-1), 2 = (0, 1,4), and (a) Prove: V is a basis. (b) Find the coordinates of (b, b2, bs) with respect to V = {71, U2, 3,}. (c) Suppose M and M' are matrices whose columns span the same vector space V. Let b be the coordinates of relative to M. Write a matrix equation that gives b', the coordinates of relative to M'. (Your answer should be a...