Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

Q: 5. (a) Consider T = LA: R³ - where A is the matrix A = R¹, T(x) = Ax 1 0 0 0 1 0 000 000 (In the…

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Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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Q: Prove that (A + B)² = -(A + B) in matrix..

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Q: Find an orthogonal matrix whose first row is (1/3,2/3,2/3)

A: The rows of an orthogonal matrix forms an orthonormal basis. Therefore, consider the extended basis,

Q: Find ∣A−1∣ for the matrix

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Q: (il, se i = j A ={ se i + j ((i + 1)', se i = j B = A = 는 se i #j

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Q: Express the matrix = [₁,1] - 9 and its inverse as a product of two elementary matrices. A =

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Q: Show that the matrix below does not have an LU-factorization.

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Q: Let A be a 2 X 3 matrix, B be a 3 X 2 matrix and v be a 3 X 1 vector. Indicate the dimensions of the…

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Q: Find a non-zero 2 x 2 matrix such that -5-2 6 15 -[88]- =

A: We have to find a non zero matrix such that the given rfelation satisfies.

Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

Q: Find an example of a 2 x 2 matrix A such that A? + I2, A3 + I2, and A6 = I2. Explain how you know,…

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Q: Show that (-A) T= -A", where A is a 2x3 type matrix (you can show it on the example)

A: Let matrix A=abcdef. Order of matrix A is 2×3. ⇒-A=-a-b-c-d-e-f ⇒(-A)T=-a-d-b-e-c-f  →Result 1

Q: Problem 8. Determine all 2x2 matrices A with the property that AB = BA, for every 2x2 ma- trix B.

A: We have to find type of matrix A which will satisfy AB=BA

Q: If A is 4 by 4 and invertible, describe the nullspace of the 4 by 8 matrix B = [ A A].

A: Given that A is 4×4 and invertible matrix. To describe the null space of the 4×8 matrix B=AA. Null…

Q: Define the variable A as a fourth order identity matrix and multiply it by a matrix B with…

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Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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Q: show that matrix  0   1      does not have LU factorization.                             1   0

A: Use the condition for the matrix to have a LU factorization.

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.