given A, Find a matrix P such that P-1AP = D, a diagonal matrix

Q: A? 0 0 A =

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Q: 34 -6 10 14. A = -[-

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Q: Express the quadratic form (c₁r1 + c₂2+...+Cnn)² in the matrix notation TA, where A is symmetric.

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Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-!AP is diagonal. (If not…

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Q: Determine all 2 × 2 matrices A such that AB = B A for any 2 × 2 matrix B.

A: Let A=abcd and B=pqrs be any 2×2 matrices.

Q: Find a QR-factorisation of 1 1 -1 1 | 1 1 1 1 0 -

A: The given question is solved below.

Q: Let A be the matrix 2 6 3 7 Find p(A). p(x) = x' – 2x + 4 i i p(A) = i

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Q: Let a matrix A has the following eigenvalues and eigen vectors 1 d1 = 3, 71 ol: 12 = 1, Find the…

A: See the detailed solution below.

Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

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Q: -2 1 2 1

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Q: A=(41] [4] ( )= (-1) [₂] + (3) [₂] 2

A: Matrix multiplication is possible if we have two matrices A and B such that, order of A =m×n;order…

Q: If A is an orthogonal matrix, find a QR factorization of A

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Q: Question : Assume that T is a linear transformation. Find the standard matrix of T OT:R² → R² first…

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Q: D = A= = Γ1 0 0 0 01 00 00 10 00 4 π 0 √2 23140 3 0 1 1 E = 27 0 5 0 0 0 √2 0 00 10 001 F = [100 0]…

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Q: Select all of the following matrices that are diagonal matrices. 1 0 0 0 0-1 0 0 0 2 0 0 0 0 0 3 0 0…

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Q: 1 1 -2 -4 A . 1 -4 and -4 4 A 1 A = ||

A: We have to solve given problem:

Q: = 1 -2 2 00 0 -1 0 0 -1

A: Given that A=

Q: Question : Assume that T is a linear transformation. Find the standard matrix of T O T:R² → R³,…

A: Any linear transformation on finite dimensional spaces can be written as a matrix format.

Q: Find A-E and the elements from the matrices

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Q: Show that for a square matrix A, AAT is a symmetric matrix.

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Q: Prove that matrix Y is obtained from matrix X. Identify the property of determinants and prove |Y| =…

A: Y=4-984261-25X=1-3-74261-25 Y is obtained from X as shown below.

Q: Let A be a 2 × 2 real matrix. Determine conditions on the entries of A so that A2 = I2.

A: Given: Let A be a 2 x 2 real matrix.   To determine: The conditions on the entries of A so that A2 =…

Q: 1 2 3 A = 1 3 2 2 6 8

A: See solution below

Q: Consider the following quadratic form; F(x, y, z) = 5x? + 2y? + 4xy + xz

A: Symmetric matrix

Q: T [2 1 -1 A + 1 = |0 5 2 4 3 8 [8 07 (b) 34" ЗАТ + 2

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Q: Find a non-zero 2 × 2 matrix A such that A2 = A =

A: We have to find a A matrix of 2x2 such that, A2  = 0000  So let suppose a matrix    Satisfy the…

Q: 3. Choose the matrix that is equal to the matrix below. 0.82 2 12 4 5 9 19 082 2 0.6 [B] 12 4 10 3…

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