Question: Let T: M2x2(R) - M2x2(R) be a linear map defined by T(A) = AT. Prove that T is diagonalizable

Let T: M2x2(R) - M2x2(R) be a linear map defined
Let T: M2x2(R) - M2x2(R) be a linear map defined by T(A) = AT. Prove that T is diagonalizable

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock 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

Students Have Also Explored These Related Mathematics Questions!

Q:

plz show me steps . ty 9 . Let T; : M2x2 ( R) > P. by T, a 2 )- (a-c)+(b+20) x+ (3c-d)x (10 pts) And T2 : P2 ( R2 by T (ax? + bx+ c)= atb Fb - 20 Determine a formula for the composition linear...

Q:

answer given questions showing all work (2) Let T : V > W be a linear transformation, and let S be a subspace of V. Prove that the set T(S) = {0: E W|T() = o: for some 6 E S} is a subspace of W. (9)...

Q:

You just need to answer e), but please well-written, Thank you! 8. Let V be a finite dimensional inner product space and let P :V + V be a linear map satisfying p2 = P. (a) Prove that the only...

Q:

Describe, and estimate the costs of, procedures to (a) insert a new item into an existing heap; (b) delete the topmost item from a non-empty heap; (c) starting from an array holding N items in...

Q:

8.4 Write on paper for upvote please. Questions: 12, 17, 22 8.4 Matrices for General Linear Transformations 485 b. Verify that Formula (8) holds for every vector in R'. d. Use the formula obtained in...

Q:

calculate below questions and provide easy step format thankyou. (1) Consider the following system of linear equations, ax - 2y +2 = I + ay + 2z = a where a E R is a parameter. (a) Classify the above...

Q:

(1) Prove or disprove : there exist a basis po, pi, p2, pa E PY(R) ( Py(R) is the set of all polynomial over real number with highest possible degree = 3 ) such that none of poly- nomials po. P1, p2,...

Q:

Consider linear transformations mapping vectors in R2 to vectors in R, clearly these are maps from a 2D vectors space to a 1D one. Since the space mapped to is one dimensional, we can call the...

Q:

[1) Consider the following system of linear equations C+ += =1 " + (b- 1 )v + 2: =1 where a and b are parameters. (a) Determine, according to the values of a and b, whether the system is compatible,...

Q:

All questions. 05:50:42 VA; 25% ' ASSIGNMENTNM1.pdf IQ 0+ Numerical Methods-Assignment-l Mathematical Prelimanaries, Taylor's Theorem, Order of Convergence (1) Let L be a real number and let {an} be...

Q:

1. In a certain locality, the magnetic declination is 0430\' East. The following magnetic azimuth of an open compass traverse reckoned from North were observed: a. Line AB, 18207\' b. Line BC,...

Q:

If the dollar interest rate is positive, explain why the value of $1,000,000 received every year for 10 years is not $10,000,000 today.

Q:

Cash Budget Cash Budget Cash Budget Cash Budget Cash Budget & Short - Term Financing Presented below are partial October, November, and December cash budgets for Holldays Events. Loans are obtained...

Q:

Year 2020 January 2020 February Month Sales ($ millions) $39,696 36,963 2020 March 34,261 2020 April 26,810 2020 May 32,045 2020 June 36,314 2020 July 38,876 2020 August 38,730 2020 September 37,231...