Parts a, b and c please! 10. For each of the following situations, provide an example...
1. Write TkuE or FaLsE for each of the following, and give a brief (specific!) justification. (i) Let A and B be square n x n nonsingular matrices. Then (AB) A- B-1 (ii) A homogeneous system of linear equations can have a unique solution. i) Suppose A is a nonsingular matrix. Then det (A-)- det(A) (iv) Diagonal matrices are always orthogonal. (v) If T and S are both linear transformations, then the linear transformation described by TS is the same...
[5] (c) Let A and B be two 3x3 matrices, and let X = Suppose further that the linear system BX = 2 has infinitely many solutions. How many solutions does the linear system have? Justify your answer! (Hint: use det(B) and det(AB).]
Please answer the parts below, thank you. A) B) C) (1 point) If A and B are 6 x 9 matrices, and C is a 8 x 6 matrix, which of the following are defined? A. B - A B. CB + 2A C. B-C D. CB E. AB (1 point) Parameterize the solutions to the following linear equation, and write your answer in vector form. -8x + 4y - 7z = -4 2 Solution: y + S +t. 2...
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original...
L. Answer True or False. Justify your answer (a) Every linear system consisting of 2 equations in 3 unknowns has infinitely many solutions (b) If A. B are n × n nonsingular matrices and AB BA, then (e) If A is an n x n matrix, with ( +A) I-A, then A O (d) If A, B two 2 x 2 symmetric matrices, then AB is also symmetric. (e) If A. B are any square matrices, then (A+ B)(A-B)-A2-B2 2....
PLEASE PROVE PARTS a and b by CONTRADICTION and solve for c as well! Could you explain your steps as well 2. (a) (10 marks) Suppose A is an n x n real matrix. Show that A can be written as a sum of two invertible matrices. HINT: for any lER, we can write A = XI + (A - XI) (b) (10 marks) Suppose V is a proper subspace of Mnn(R). That is to say, V is a subspace,...
answer all parts Figure 3: A rotating shaft with the welded homogeneous solid cube of mass m with the size of the edge 2a. 6. A weightless (light) shaft AB of length 6a has a homogeneous solid cube of mass m with the size of the edge equal to 2a welded to the shaft along the edge CD, see Figure 3. The system is supported by bearings at A and B and rotates about AB at 2 radians per second....
Help me plz to solve questions a and b 9. (10pts) Answer only four parts by True/False and provide justifica- tions] Given A, B and C three n × n matrices: (a) If C'is a nonsingular skew-symmetric matrix, then its inverse is also skew symmetric b) If rank(A) and AB- AC then B- C c) Let S-V, V2, Vs) be a lnearly independent set of vectors in a vector space V and T V2, V2+Vs, ViVs); then T is linearly...
sorry I thought it would look for similar questions after taking a picture. but it posted I also need help with these questions plus what the picture had. Thank you! d)deduce that the matrix A is invertible e) solve the linear system S1 by Gauss Elimination f) find the inverse A^-1 of A g)deduce the solution of S1 h) find the LU decomposition of the matrix A I) solve the linear system of equation S1 by using the LU j)...
Hi im struggling with part (b) and (c) of this linear algebra question. Any help would be greatly apprecated (a) Write down the augmented matrix corresponding to the system of linear equations: + 25 3w W W - + + y y + 1 Na + 4 [2 marks (b) For the remainder of this question the variables v, w, 2, y, and 2 will satisfy a system of linear equations whose augmented matrix is Ab). If the reduced row...