Suppose S is a real symmetric matrix, H is a complex Hermitian matrix, P is a real orthogonal projection, and i is non-zero. Which of these statements are true? 1. ito-sQ is diagonal, then Q has orthogonal columns. True False 2. There is a matrix Q with OT HO diagonal. D 3. If i and w are eigenvectors of S is different eigenspaces, then (6, w) 0. B 4. Every eigenvalue of P is -1 or 1. 5. If SE = A0, then Å ER. B 6. If Hi = d0, then |A = 1.

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A: It is given that {Av1,...,Avn} is linearly independent. We will prove that A is nonsingular.

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Q: .

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A: If A and B are singular  matrices the A+B is also singular. (False Statements)

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A: We shall solve first question only as you have asked more than one Que of same type. For others…

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Q: 4. (a) Show that the following matrix is diagonalizable. (b) Find a matrix P that diagonalizes A.…

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