--- (c) Let A = 2 1 -1 0 1 Find an orthogonal matrix P such that PTAP = D where D is a diagonal matrix D. Show your calculation clearly and check your answer.]

Q: -2 6. What is the diagonal matrix Find an orthogonal matrix Q that diagonalizes A = 6. A?

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Q: Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

A: Describe y as the sum of vertices x1 in span u and x2 orthogonal to u         x1=α9, 3=9α, 3α and…

Q: Construct a matrix that stretches vectors in the direction V₁ = 22-Ĵ by a factor of 4 and leaves…

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Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: A matrix A € Rmxn can also be viewed as a vector, by stacking all its n columns into a single…

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Q: LOT A = [ ₁ - 10 Let 1 D= 0 1 1 -1 1 Construct a 4x2 matrix D, using only 1 and 0 as entries, such…

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Q: Let 0 9. A = = [6 0 Is it possible to find a two by two real matrix B such that A = eB₂

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Q: Find the projection matrix P, and the projection of b= (1,2,3) onto 2. Let A= -1 -1 the column space…

A: Given matrix is A=1001-1-1

Q: 1 Find the linear combination 2$1 +382 + 4s3 b. Then write b as a matrix-vector multiplication Sx.…

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: Use the definition of A to write the vector equation as an augmented matrix. 0 x₁ + x2 + x3 + X4 =

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Q: Find ∣A−1∣ for the matrix

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Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: Q2) In each of the following cases, find the matrix A for which [v]D=A[v]B a. B={1, 2x, 4x²-1} and…

A: Here we use the definition of the change of basis matrix. For that we first write the basis elements…

Q: Find the following matrix-vector product: [13 20 0 -1 3 -2

A: The given matrices

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

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Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

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Q: Find Jordan form of this matrix

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Q: Let 3 A = -1 -1 3 -1 -1 3 (a) Find a matrix P that orthogonally diagonalizes A. (b) Find B = P-¹AP…

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Q: 1 -1 2 a) Find the matrix A if (3A) =0 2 0 3 -1 4

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Q: 1 6. Given that A = -1 and B = Which of these matrices equal (AB)'? -2 0 (c) 0. (a) 0. (b) (d) -2 -2…

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Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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Q: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

A: Uf7ygth

Q: Properties of Transpose If r is a scalar and A and B are matrices of the appropriate sizes, then 1.…

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.