Question: Show that if A is any n n matrix, then (a) A + AT is symmetric. (b) A - AT is skew symmetric.

Show that if A is any n × n matrix, then
(a) A + AT is symmetric.
(b) A - AT is skew symmetric.

Step by Step Solution

★★★★★

3.36 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a A A T T A T A T ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

951-M-L-A-L-S (6790).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Show that if A is any m n matrix, then Im A = A and AIn = A.

Q:

Show that if A is a symmetric, idempotent matrix, then A+ = A.

Q:

Show that if A is n ( n with n odd and skew symmetric, then det(A) = 0.

Q:

Show that if A is an n n matrix, then A = S + K, where S is symmetric and K is skew symmetric. Also show that this decomposition is unique.

Q:

Let X be any n k matrix. Show that XrX is a symmetric matrix.

Q:

Show that if A is an n n matrix, then AAT and A + AT are symmetric.

Q:

Linear Algebra Question a. Show that the determinant of a upper triangular n n matrix is the product of the diagonal entries. 6. Show that the determinant of a n n matrix A which is in RREF is...

Q:

(a) Let A be an m n matrix with a row consisting entirely of zeros. Show that if B is an n p matrix, then A B has a row of zeros. (b) Let A be an m x n matrix with a column consisting entirely of...

Q:

a. Show that if A is an n n matrix, then where i , . . . , n are the eigenvalues of A. b. Show that A is singular if and only if = 0 is an eigenvalue of A. det AT.

Q:

Show that each eigenspace of an n n matrix A is an invariant subspace, as defined in Exercise 7.4.32. Exercise 7.4.32 The subspace W of a vector space V is said to be an invariant subspace under the...

Q:

Name the ten project management knowledge areas and briefly summarize each.

Q:

Give at least two examples of asset-backed securities.

Q:

13.57 Example 11.3 (p. 418) presented data from a study in which sedentary men were randomly assigned to be placed on a diet or exercise for a year to lose weight. Forty-two men were placed on a...

Q:

Use the data in SDATA.XLS and statistical software to run the following regression: where GPA = grade point average and ST = study time per day (A) Interpret the value you obtained for 0. (B)...

Q:

Let Assuming that det(A) = - 7, find (a) det(3A) (b) det(2A-1) (c) det ((2A)-1) (d) adg a g d

Q:

Without directly evaluating, show that b+c c+a b+a det a

Q:

Find the number of inversions in each of the following permutations of {1, 2, 3, 4, 5}. (a) (4 1 3 5 2) (b) (5 4 3 2 1)

Q:

K-Too Everwear Corporation can manufacture mountain climbing shoes for $25.70 per pair in variable raw material costs and $16.95 per pair in variable labor expense. The shoes sell for $126 per pair...

Q:

During his speech to the AGM, the Chairman of Banks DIH stated the company was able to achieve an EBIT of 100, depreciation on assets was 40 , interest paid on financing facilities was 20 and final...

Q:

Chef Gourmet, Inc., has assembled the following data pertaining to its two most popular products. Blender Food Processor Direct material $ 24 $ 28 Direct labor 17 45 Manufacturing overhead @ $58 per...