1 -1 1 -1 1 1 A = 2 1 1 1 , compute the rank of A:, i.e. r(A) 3 1 1 0 1 3 0 5

Q: Let 1 5-1 A = 0 1 0 and P = 0 0 0 15-2 05 Given that P diagonalizes A, then compute A¹¹. i A" i i

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Q: 4) Let a, b, and c be real numbers and consider the second order ODE ax"(t) + bx' (t) + cx(t) = 0.…

A: Let y1=x                            ...(1)Let y2=x'                            ...(2)Differentiating…

Q: Show that f(z)dr: S(#2-2) +4f(r2i-1) + f(#2)]- an"(c.)} m-1 h4 (0) +2f(2) + 4f(*2-1) + f(*) I80(6 -…

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Q: -1 Express the general solution of Ax = b where A = 3 and 3 1 as x = x, + cx, where x, is the row…

A: It is given that, Ax=b where, A=-1-133 and, b=1-3

Q: -2 Let y = what are the expansion coefficients of y in the basis {vo, V1, V2 , v3 } you found in the…

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Q: 2. Let g (x, y) = 2a² – y² . Compute g (1, 2), g (2, 1), g (1, 1), g(–1, 1), and g (2, – 1). - £(1…

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Q: -6 Express the general solution of Ax =b where A = and 6 -12 -6 as x = x, + cx„ where x, is the row…

A: Given: Matrix A=3-66-12 and B=-6-12. The objective is to express the general solution of Ax=b.

Q: 1 3 S = 4 9. a basis for R3? Explain why or why not.

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Q: -3 0 1 1 1 2 -4 1. Let A = -2 1 -6 3 -4 2 Compute det(A) using cofactor expansion. Indicate the row…

A: Given  A=112-3-40-10-21-6032-42

Q: 7. Let T1 : R² R$, and T2 : R$ R² be given by: T1((x, y)) = (x + 2y, 3x – y, 5x + 7y, 6y, –2x ), and…

A: See the attachment

Q: 1 1 0 k- 4 -k + 5 is not diagonalizable over C. k (Enter your answers as a comma separated list.)

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Q: -2 -8 -31 A = -3 -8 -29 24 90 (a) Compute det(A) = (b) Use Cramer's rule to solve the following…

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Q: If z = 1-j3,Z2=-2+j5 and Z=-3- j4, determine in a + jb form: (a) ZZ (b) (c) Zi + Zz (d) Z,ZZ

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1 -2 1 2 Let A= 1 -1 -4 -2 5 1 (a) Find det(A). (b) Is A singular? Justify.

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Q: Let 6. 0 9 11 -2 1 3 4 8 A = 6 9 0 0 0 What is the rank of AT A?

A: Given matrix is A=650911-2001348000604000090000000

Q: Let y = 2 1 what are the expansion coefficients of y in the basis {vo, V1, v2 , v3 } you found in…

A: In the Previous question, the vectors v(3) that is forms an orthonormal basis in R4, The vector are…

Q: -1 2 1 Let A Compute AAT and AT A. 1 0 1 1 -1

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Q: 3 1 -4 1 -3 A = -1 & & B = Find ??? 1- Prove that At + Bt + Ct = (A +B + C)t %3D 2- Prove that (B *…

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Q: х — у — 2 T: R3 → R3 such that T Find bases for the range space and 2х + 3у + 2 За — 4у — 2х kernel…

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Q: 2. Determine all k e R for which A is diagonalizable. [1 k 1 (a) A [1 0 k (b) A= |0 1 0 0 0 k

A: Solve the following

Q: Find the string that has this generating function: a) (1− x)−3 b) (1+2x)−4 c) 1/(1 −3x)3

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Q: 5 Find w if (w)s = |0| relative to the basis S = {-3 -5 2 } 2 3 w =

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Q: 2. Let g (x, y) = 2x² – y² . Compute 9(1, 2), g (2, 1), g (1, 1), g (–1, 1) and g (2, –1).

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Q: 6. 2 87 5. Let A=-3 4 1 4 -4 5 a) Find adj A. b) Compute det(A). c) Show that A(adj A) = (adj A)A=…

A: To solve the following problem

Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

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Q: What equation does this set of algebra tiles represent? 1 1 1 1 1 1 1 1 1 1 -X-x-x 1 1 1 1 1 %3D 1 1…

A: Given: On the left-hand side, there are 3 red variable(x) tiles with 6 unit tiles. On the right-hand…

Q: 1 1 0 k-1 -k +2 is not diagonalizable over C. k = (Enter your answers as a comma separated list.)

A:

Q: ch of the following shows the structure of Earth in the A. core, crust, mantle, landform, water B.…

A: We will use basic of geography. Solution of the above question is in the step below.

Q: 3 2 1 2] 1 1 0 2 0 3 1 1 Compute the inverse of A = by finding adj(A). %3D 1 0 0 1]

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Q: 2 31-1 What is the dimension of the null space Nul(A) of A = |0 0 4 0? 0 0 0 0

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Q: f. Both H and J below have their leading 1 in row 3 in the same column: 1 0 0 6. 7 1 0 0 -2 9. H 0 1…

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Suppose T ∈ L(V ), m is a positive integer, and v ∈ V is such that Tm-1v does not equal 0 but Tmv=0.…

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Q: 10. S = {r² + 3r + 1,2r² + x – 1, 4r + 1} is: %3D a. a linearly independent set of P2. b. a linearly…

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Q: Let -1 15 0 1 -1] and P =0 01 1 1 5 A = 0. %3D 0 15 -2 105 Given that diagonalizes A, then compute…

A:

Q: 1 -1 Find a mat rixP such that P-1 2 1 0 2 1 P = O A. 0 1 -1 0 O B. 1 1 1 0 P = C. 1 1 1-1 P = D. 1…

A: In this question we have to find Matrix P

Q: (a) g: Zg → Z6 defined by g(n) = n 2. (b) g: Z6 → Z6 defined by g(x) =x €x. (c) g: Zs → Zs defined…

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Q: 1 0 -1 Let A = 0 2 2 and A | y 2. Then in applying 1 2 3 Cramer's Rule, we need to compute 1 0 2 2…

A:

Q: |-1 7 -1 Let A= 0 11 1 1. and P= 0 0 1. Given that P diagonalizes A, Compute A11. 1 15 -21 101

A: We have to find A ^11

Q: Example 6.20. Using the method of separation of symbols, prove that (i) u „x + u,x + ux³ Ди, + A?u,…

A: Here, We need to use method of separation.

Q: Exercises 8. T:R² → R² defined by T(x1,x2) = (ı+x2, x1 – x2 – 1). 9. T:R? → R° defined by T(x1,x2) =…

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Q: Question 2: For which real values of a do the polynomials P1(t) = at² – t -; P2(t) = -t² + at – ;;…

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Q: 2 3 Let A = -1 2 3 -2 1 (a) Find adj A. (b) Compute det(A). (c) Verify Theorem 3.12; that is, show…

A: A=213-1203-21 We need to find adj.A det(A) Verify Aadj. A=adj. AA=detAI3

Q: Let A = -1 0 and P 1 -1 1 | Given that P diagonalizes A, then compute each of the following powers…

A: We are asked to find the given matrix.

Q: 2 17 1 12 7 15 2] What is the coefficient of X in the characteristic polynomial of the matrix A =…

A: Given matrix 5211127152Form a new matrix by subtracting λ from the diagonal…

Q: s = (6 4 1) (3 −5 1) (8 13 6) (0 6 9) explain why S is not a basis for R3

A: Given S=6,4,1,3,−5,1,8,13,6,0,6,9. We have to explain why S is not basis of R3. Definition:- The…

Q: 3 3 17 Let A=3 %3D 2 2 1 3 compute det(A) using cofactor-expansion (down the first column).

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Q: Reduce Z= ( 1+i) (1+i) / (1-í), to the form a + ib -1-i .a 1-i .b 1+i .C -1+i .d others .e

A:

Q: Let 1 5 -1 1 1 0 0 0 1 A = 1 and P = 0 15 -2 1 05 Given that P diagonalizes A, then compute A** Al1…

A: We have A=-15-1010015-2 and P=110001105 We have that P diagonalizes A. This means A is similar to a…

Q: The value of a' for which f : R → R, ax +7 flx) is invertible lies in %3D 2 x* +4 (а) (0, 2) (b) (1,…

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Q: х — у — 2 2х + Зу + 2 Зх — 4у — 2г T: R³ → R3 such that T Find bases for the range space and kernel…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.