1. For the following two matrices A = 1 2 3 4 B = 1 3...

1. For the following two matrices
A = 1 2
3 4
B = 1 3 5
2 4 6
Find:

a). AB, is AB = BA ?
b). All row and column vectors of A and B

2. Let X1=[1, 0, 0], X2=[0, 3, 0], and X3=[0, 0, 2], use definition of linear dependency to
show that the above three vectors are dependent or not.

3. Show that the following matrix is singular or nonsingular, and find A-1 if possible.
A =
1 2 3
3 2 1
2 3 1

Expert Solution

Colby Messinger answered 7 months ago

Let A and b be the matrices A = 1 2 4 17 3 6 −12...

Let A and b be the matrices A = 1 2 4 17 3 6 −12 3 2 3 −3 2 0 2 −2 6 and b = (17, 3, 3, 4) . (a) Explain why A does not have an LU factorization. (b) Use partial pivoting and find the permutation matrix P as well as the LU factors such that PA = LU. (c) Use the information in P, L, and U to solve Ax = b

Find the dimensions of the following linear spaces. (a) The space of all 3×4 matrices (b)...

Find the dimensions of the following linear spaces. (a) The space of all 3×4 matrices (b) The space of all upper triangular 5×5 matrices (c) The space of all diagonal 6×6 matrices

a. Using Matlab scripts create the following matrices (???1 and ???2) ???1 = [ 3 2...

a. Using Matlab scripts create the following matrices (???1 and ???2) ???1 = [ 3 2 −3 6 7 4 3 −6 7 ], ???2 = [ 2 1 7 3 3 9 −6 6 1 ] b. Write code to add the second row of ???1 to the third row of ???2 and store results in the first row of ???1. c. Write code to add the second column of ???1 with the third column of ???2 and...

Apply ?̂2 and ?̂?operator on the following wavefunctions, a. ( 3 4? ) 1/2 ???? b....

Apply ?̂2 and ?̂?operator on the following wavefunctions, a. ( 3 4? ) 1/2 ???? b. ( 3 8? ) 1/2 ???? ? ?? c. ( 3 8? ) 1/2 ???? ? −?? What is the result? Which is these functions are eigen functions of both operators? Is there anything else you like to conclude?

Prove that if A and B are 2x2 matrices, then (A + B)^(2) = A^(2) +...

Prove that if A and B are 2x2 matrices, then (A + B)^(2) = A^(2) + AB + BA + B^(2). Hint: Write out 2x2 matrices for A and B using variable entries in each location and perform the operations on either side of the equation to determine whether the two sides are equivalent.

1. Find all eigenvalues of each of the following matrices. (a) |10 −18 b) |2 −1...

1. Find all eigenvalues of each of the following matrices. (a) |10 −18 b) |2 −1 (c) |5 4 2 6 −11 | 5 -2| 4 5 2 2 2 2|

Which of the following are true? (1) The sum of two invertible matrices is invertible (2)...

Which of the following are true? (1) The sum of two invertible matrices is invertible (2) The determinant of the sum is the sum of the determinants (3) The determinant of the inverse is the reciprocal of the determinant (4) An nxn matrix is invertible if and only if its determinant is zero (5) The product of two invertible matrices is invertible (so long as the product is defined) (6) If A is a diagonal 3x3 matrix [a,0,0;0,b,0;0,0,c] then its...

Consider two assets, A and B. A earns +4%, –5%, or +3%, in scenarios 1, 2,...

Consider two assets, A and B. A earns +4%, –5%, or +3%, in scenarios 1, 2, and 3. B earns –5%, +3%, or +4%, in scenarios 1, 2, and 3. Compute the expected rates of return and SD for each asset, A and B. Now, consider a portfolio of assets A and B called AB, where the investor holds fraction 62% of his portfolio in A and fraction (1-62%) in B. Compute the standard deviation of AB and report this...

The following page-reference string: 1, 2, 4, 3, 2, 5, 4, 2, 4, 2, 1, 3,...

The following page-reference string: 1, 2, 4, 3, 2, 5, 4, 2, 4, 2, 1, 3, 2, 3, 1, 3, 6, 1, 6, 4. Main memory with 3 frames of 1 kilobyte available and they are all initially empty. Complete a figure, similar to Figure 8.14(in the slides or textbook), showing the frame allocation for each of the following page replacement policies: a. Optimal b. Least recently used c. First-in-first-out Then, find the relative performance of each policy with respect...

for square matrices A and B show that [A,B]=0 then [A^2,B]=0

Question