2. Given that u., and ware three solutions of the linear system Az = b. Verify...
1. Let A and B be two nx matrices. Suppose that AB is invertible. Show that the system Az = 0 has only the trivial solution. 5. Given that B and D are invertible matrices of orders n and p respectively, and A = W X1 Find A-" by writing A-as a suitably partitioned matrix B
1. Let A and B be two nx matrices. Suppose that AB is invertible. Show that the system Az = 0 has only the trivial solution. 5. Given that B and D are invertible matrices of orders n and p respectively, and A = W X1 Find A-" by writing A-as a suitably partitioned matrix B
SOLVE BOTH 2 and 3 2. Given that u,v, and w are three solutions of the linear system Az = b. Verify that the vector cu + dv + (1-c-d)w is also a solution of Ax = b for any scalars c, d ER 3. Let A= -21 1 - 2 1 -2 Determine whether the system Ar = b is consistent for every beR'.
SOLVE BOTH 4 and 5!! 4. Let A and B be two nxn matrices. Suppose that AB is invertible. Show that the system Ar 0 has only the trivial solution 5. Given that B and D are invertible matrices of orders n and p respectively, and A = Find A by writing A as a suitably partitioned matrix
2. Given that u, v, and w are three solutions of the linear system Ax = b. Verify that the vector cu + dv + (1 − c − d)w is also a solution of Ax = b for any scalars c, d ∈ R.
2. Given that u, v, and w are three solutions of the linear system Ac = b. Verify that the vector cu + dv + (1 - C-d)w is also a solution of Ax b for any scalars c, d E R.
[B0 5. Given that B and D are invertible matrices of orders n and p respectively, and A [W X Find A- by writing A-1 as a suitably partitioned matrix Y Z
Гв C D 5. Given that B and D are invertible matrices of orders n and p respectively, and A = (W x] Find A-? by writing A-1 as a suitably partitioned matrix LY Z
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...
1. Verify that the following linear system does not have an infinite number of solutions for all constants b. 1 +39 - 13 = 1 2x + 2x2 = b 1 + bxg+bary = 1 2. Consider the matrices -=(: -1, -13). C-69--1--| 2 -1 0] 3 and F-10 1 1 [2 03 (a) Show that A, B, C, D and F are invertible matrices. (b) Solve the following equations for the unknown matrix X. (i) AXT = BC (ii)...