• Verify that the new basis is orthogonal and find the transformation matrix • Find the tensor F has the compoments 2 -2 0 -2 6 4. referred to the system e,, find its compoments in the system e.

Q: 2. Find an orthonormal basis for the image (column space) of A, where 1 2 3 A = 2 4 6 3 6 0

A: A=123246360  ~ 12300000-9 R2→R2-2R1R3→R3-3R1 ∴it for only first and 3rd column leading coefficient…

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Q: Examnple: Determine the Gersgorin disks for the matrix 4 1 A = 2 2 -2 0 10

A:

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A: We create a matrix A as  A=134224533210 Orthogonal of A = 134524533210|A| Eigen space…

Q: Orthogonalize the basis {(1, 1, 1, 1),(1, 1, −1, −1),(0, −1, 2, 1)} by the Gram-Schimidt process.…

A: Let x1 = 1111 ; x2 = 11-1-1 ;  x3 = 0-121      Using Gram schmidt process , we get orthogonal…

Q: Find an orthogonal basis for the column space of the matrix to the right. -1 2 -8 4 1 -2 7 1 - 4 - 3

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Q: Find the global transformation matrix to transfer the local coordinate system (x1, y1, Zı) to the…

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Q: Determine whether the matrix is orthogonal. An invertible square matrix A is orthogonal when A-1 =…

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Q: 3. Write matrices for an x-shear with shear factor -2, a rotation of 180, an enlargement of scale…

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Q: 4 9. ー4 3. 4 4 2. 9 Find column ortho gonal basis for the an Space of the matrix abeve. %3D

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Q: Let S = and T = be ordered bases for R2. Let v = and w = (a) Find the coordinate vectors of v and w…

A: Given: S=12,01 T=11,23 v=15 w=54 (a) Let v=a11+b2315=a11+b23. Then, a+2b=1 and a+3b=5, On…

Q: 4. Make a 3x3 unitary matrix of your cholce (or choose from any book), find Its elgen values and…

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Q: What is the transformation matrix T for the case below? If position vector is given as Poye = [0 0…

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Q: 3. Determine standard matrix for each of the linear operator T: R R reflection about yz-plane…

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Q: Find a basis of the kernel of the matrix 1 2 03 5 0 0 146 Justify your answer carefully; that is,…

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Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". 3 10 -), (o, 1, 0), 0, 10…

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Q: Find a basis for R3 that includes the vectors (1, 0, 2) and (0, 1, 1).

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Q: The Gram-Schmidt process transformsthe basis u1=(-3,1), u2=(7, 1) of R´ into the orthogonal basis…

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Q: (a) Find the coordinate vector of z 3 with respect to the ordered basis of R (b) Let F, be the…

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Q: Use Gram-Schmidt to find an orthogonal basis for R' if B={(2, -5), (1, 3)}.

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Q: a. Find the change of basis matrix from the basis B to the basis C. [id] = b. Find the change of…

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Q: Rrotates points about the origin through- radians and then reflects through the ne linear…

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Q: 5. (a) Show that the vectors u1 = (3, 1,0), u2 = (-1,3,0) and uz = (0,0, 4) form an orthogonal basis…

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Q: The Gram-Schmidt process transforms the basis u=(-1,3), u2-(7,-1) of R into the orthogonal basis…

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Q: 1 -2 -4 -2 -1 4 1 4 3 -2 0 2 -1 0 9. 4

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Q: Find the basis of column space of the matrix A given in the attached image .Please answer quickly .

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Q: Let B': f1+2x,3-x} And B = {1,x? be Basis for Pi Find the Transi tien matrin Pa-aB' Bae' denote…

A: Consider the provided question, Given, B'=1+2x, 3-x and B=1, x We need to find the transition matrix…