[1 Find a matrix A = -4 -51 = l3. y] 1 z such that A² 10 %3D Lo 1. Lo

Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

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

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Q: Find a 2 by 2 matrix that reflects the point (x,y) abot the x axis?

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Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: Find a 3 by 3 matrix that scales the point (x,y,z) by 2 in the x direction and 4.5 in the direction,…

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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: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

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

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Q: -1 -1 | | 4. For the semidefinite matrix A = -1 2 -1 write x' Ax as a -1 -1 sum of two squares.

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Q: Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

A: To find: dimcol(A)⊥ Given information: A is 8×4 matrix such that rank(A)=3. Concept used:…

Q: Let C be a 5 x 7 matrix with a rank 4. (1) What is the dimension of the solution space of Ax 0?

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Q: 1 1 -4 -2

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Q: (2) Consider the matrix -[: ] A = Find the unique x, y E R, such that A? = xA – yI (where I…

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Q: Find the 3x3 matrix that induces the described action on R3. Rotates the xy plane by 30 degrees,…

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Q: Find a 2 by 2  matrix that scales the point (x,y) by 0.5 in the x direction and 3 in the y…

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Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -1…

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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: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001

Q: Find the 3x3 matrix that induces the described action on R3. Rotates the yz plane  by 45 degrees,…

A: We have to find 3×3 matrix that rotates the yz plane by 45 degrees and reflects the x-axis.

Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

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Q: Find an explicit description of NulA by listing vectors that span the null space, where [1 5 -4 -3…

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Q: [1 0 1] Q2. Is the matrix A = 0 1 1 defective or diagonalizable? If diagonalizable, write the…

A: We have to solve given problem:

Q: -37 -1 0 -1 4 0 -1 -1 4 -1 0 A = 3

A: Here we use the gram Schmidt process to find the QR decomposition of matrix

Q: Let A be a 2 x 2 matrix a If ad – bc + 0, then A-1 ad-be ad-be ad-e ad-be. such that [1 AA-1 = A-'A…

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Q: Express the matrix A-¹ as a product of elementary matrices using In= EkEk-1...E₁A. 100 220 313 A =

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Q: Let A be 3 x3 R given matrix by over 2. A = -1 Using the result of A find the value (s) of makes the…

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Q: 5 3 [B] -5 -6 i.e. write A = LU where L is a lower triangular matrix with 1's on the diagonal, and U…

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Q: 3 x 3. Find A² - 5A + 4I3, if A = -2 1 0 -1 43 0 85 where I3 is a unit matrix of order

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Q: If x=2:2:6, and y=[1, 3, 7]. Write the values of the matrix A=[x' y'] where ' is a matrix transpose.

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Q: Write down the 3 x 3 matrix that rotates a 2D point by angle about a point 0 p = (xp, yp).

A: Consider point .To write the  matrix that rotates a  point by angle  about a point .

Q: Find the hessian matrix for y = x12 + 2x22

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Q: Find a 3 × 2 matrix A and has LU factorization where L is diagonal.

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Q: (a) Describe the kernel and the image of Jn. (b) Use this to show that J, is diagonalisable when n #…

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Q: Suppose T: R² → R4 is a linear transformation with T(₁) - (standard) matrix A such that T(x) = Ax.…

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