Question

6. Let A be an Orthogonal 3 !! 3 matrix, B a 3 !! 3 matrix such that det B = -5 and C = -3A^T B^3 A Evaluate det C. 7. (a) Find real numbers x, y, and z such that the matrix Q is Hermitian, where Q = [ 3 x + 2i yi 3 - 2i 0 1 + zi yi 1 - xi -1 ]. (b) Show that the matrix U is unitary, where U = [ 1/?2 (i-1)/2?2 (i+1)/2?2 0 i/?2 -1/?2 i/?2 (i+1)/2?2 (1-i)/2?2 ].

          6. Let A be an Orthogonal 3 !! 3 matrix, B a 3 !! 3 matrix such that det B = -5 and C = -3A^T B^3 A Evaluate det C.

7. (a) Find real numbers x, y, and z such that the matrix Q is Hermitian, where

Q = [
3 x + 2i yi
3 - 2i 0 1 + zi
yi 1 - xi -1
].

(b) Show that the matrix U is unitary, where

U = [
1/?2 (i-1)/2?2 (i+1)/2?2
0 i/?2 -1/?2
i/?2 (i+1)/2?2 (1-i)/2?2
].

6. Let A be an Orthogonal 3 !! 3 matrix, B a 3 !! 3 matrix such that det B = -5 and C = -3A^T B^3 A Evaluate det C.

7. (a) Find real numbers x, y, and z such that the matrix Q is Hermitian, where

Q = [
3 x + 2i yi
3 - 2i 0 1 + zi
yi 1 - xi -1
].

(b) Show that the matrix U is unitary, where

U = [
1/?2 (i-1)/2?2 (i+1)/2?2
0 i/?2 -1/?2
i/?2 (i+1)/2?2 (1-i)/2?2
].

Added by Bethany S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/08/2023

Step 1

This can be done by multiplying both matrices together and then taking the determinant of the result. Det B C = (-3AT B3A) Show more…

Show all steps

Thanks for your feedback!

6. Let A be an Orthogonal 3 !! 3 matrix, B a 3 !! 3 matrix such that det B = -5 and C = -3A^T B^3 A Evaluate det C. 7. (a) Find real numbers x, y, and z such that the matrix Q is Hermitian, where Q = [ 3 x + 2i yi; 3 - 2i 0 1 + zi; yi 1 - xi -1 ]. (b) Show that the matrix U is unitary, where U = [ 1/√2 (i-1)/2√2 (i+1)/2√2; 0 i/√2 -1/√2; i/√2 (i+1)/2√2 (1-i)/2√2 ].