1. Let A be the matrix given below, in which a and b are real numbers. 0 0 b 0 a a 0 00 a 0 0 0 b 0 A = (a) Find all values of a and b for which A is diagonalizable. (b) For any values for which it is diagonalizable, diagonalize it (meaning find the invertible P and diagonal D such that A = PDP-¹).

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Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

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A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

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A: Step 1:   Step 2: Step 3: Step 4:

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