Consider the following real symmetric matrix 1 1 1V 1 -1 1 1 1 -1 a) find the eigenvalues b) find the eigenvectors c) show that eigenvectors are mutually perpendicular (do it for any of the two vectors)

Q: Show that any 3 × 3 matrix of the form ⎧ ⎩ a 1 0 0 a 1 0 0 b ⎫ ⎭ is defective.

A: We have to show that given matrix is defective.

Q: Characterize the image and kernel of the following matrices: 1 (443) -2 2 2

A:

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A:

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A: Size of matrix is same as order of matrix

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A:

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Q: [1-2 Q:Evaluate A-3A+91 where A = 2 3 3 -1 and lisa unit matrix. -3 1 2 3.

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Q: 2 3 10 2 A = 5 4 9 2 3 1 3 multiplying the matrices, explain why A is not invertib

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Q: Find a basis for the row space of the matrix 1 1 02 2 2 2 2 -1 -2 0 A -1 -1

A: Given that the matrix is:                      To find a basis for the row space of the given matrix…