7 1 A= B= 2 2 3 1 3 4 1/2 3/2 1 1 D= 5/6 113 E 3 6 4 3 Σ 1 2 4 2. 1, 4.

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: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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Q: A function y = f (x) is represented parametrically as follows: x= (t)=t-5t- 20t +7 y = v (t)=…

A: We will find out the corresponding extremum for given function. Kindly note that there is a misprint…

Q: 3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and…

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Q: Let B = {1, cos t, cos? t, cos t, cost t} and C = {1, cos t, cos 2t, cos 3t, cos 4t} and assume the…

A: Given B=1,cost,cos2t,cos3t,cos4t and…

Q: Evaluate: Use 3 decimal places [1 9' 10 b =|0 1 4 o] 4 -3 A = | 8 -4 12 -8] Find the value of the…

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Q: By Using Matrix find (T1 ' T2 ' T3 ' T

A: Augmented matrix of the given system is  -4101-1201-410-13001-41-40101-4-30

Q: Let B = matrix from B to C 8 - { }], ] } and c-{[7], [43]} C = be two bases for R². Find the change…

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Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Let ū= (a) 2T Calculate projcol Au for the following matrices A: A = - (b) A = 0

A: Column Space: A set of vectors that spans the columns of a matrix A is called the column spaceof A…

Q: A) Justify if the matrix A is diagonalizable.B) Find a matrix T and a diagonal matrix J, such that…

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Q: det (–3(A" A-²)*) Consider matrix A of order 3, the value of corresponds to: 1 a) –7 - 1 b) –3 c) –3…

A: For the solution of the problem follow the next step.

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

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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 be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

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Q: 1 2 A = 0 1

A: Given that A=1201 First to find the Jordan canonical form of this matrix: The given matrix is a…

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: 3) Let A = 2 -1 Find a matrix P that orthogonally diagonalizes A. Use P to com- 0 -1 pute A5.

A: Given, A=11012-10-11first we have to find a matrix Pfor eigen values of…

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

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Q: Consider the matrix, 0 A = 1 0 a) Write A as a product of elementary matrices. b) What is the…

A: Solution is here

Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

Q: Let B = {b1,b2} and C = {c1, C2} be R². Produce the change-of-coordinate matrix from B to C and from…

A: The change of basis matrix form B to C (or from the basis B to the basis C ) and C to B where B and…

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: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

A: We have to find all real numbers  for which the matrix  is diagonalizable in

Q: If A is a 2x2 matrix such that trace(A) = det(A) = 3, then what is the %3D value of trace of (A-!) ?…

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Q: find if the vector x is in the range for matrix A

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Q: b7 c d x A = j g _e f] a If then size of matrix A: %3D

A: Here we find size of Matrix A ?

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

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Q: 1 2 Let A = 4 1 a) Write A-1 as a product of elementary matrices. b) Using A-1, solve XA= B for the…

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Q: ey = 25e4x-z+w 10z - w + 3x = -23 8y + 3w - x -z = 5 x+y-z + 4w = -10

A: The objective is to rearrange the  equations so that their associated matrix is ​​diagonally…

Q: 13. Find all 2 x 2 matrices A = (" such that A? %3D

A: Image is attached with detailed solution.