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JA Let ₁ Select one: 0 a Ob (-)- Oc subspace W- Span (x₁, x₂) of R³. Let y = Od and x₂ = () ŷ-projw (y) - -13/38 ŷ-projw (y) = -22/19 -55/38 ŷ= projw (y) = Note that x, and x, are orthogonal and therefore form an orthogonal basis for the -1/2 -1 -3/2 -4/45 ŷ= projw (y) = -17/45 -4/9 3/19 -3/19 1/19 () What is the orthogonal projection projw (y) of y onto W?

JA Let ₁ Select one: 0 a Ob (-)- Oc subspace W- Span (x₁, x₂) of R³. Let y = Od and x₂ = () ŷ-projw (y) - -13/38 ŷ-projw (y) = -22/19 -55/38 ŷ= projw (y) = Note that x, and x, are orthogonal and therefore form an orthogonal basis for the -1/2 -1 -3/2 -4/45 ŷ= projw (y) = -17/45 -4/9 3/19 -3/19 1/19 () What is the orthogonal projection projw (y) of y onto W?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hax tion () subspace W = Span {x₁, x₂) of R³. Let y = Let x₁ = Select one: O a O b. Oc O d. -13/38 ŷ projw (y) = -22/19 -55/38 ŷ-projw (y) = and x₂= ŷ = projw (y) = 4/45 ŷ projw (y) = -17/45 = -4/9 Select one: O a Oc ○b. J(Y) = O d. J(Y₂) = -1/2 -1 -3/2 Ponsider th Consider the following nonlinear system of differential equations at (x, y) = (1, 0) (which could also be written as a column vector Y₁ = J(Y) = J(Y₂)= 3/19 -3/19 1/19 Note that x, and x₂ are orthogonal and therefore form an orthogonal basis for the (1³) 0 (²) 3 -5 3 (1³) 0 3 -5 -5 What is the orthogonal projection projw (y) of y onto W? N&HE -z + 3y -5y This system has an equilibrium point Which matrix is the Jacobian matrix J(Y)?
Transcribed Image Text:Hax tion () subspace W = Span {x₁, x₂) of R³. Let y = Let x₁ = Select one: O a O b. Oc O d. -13/38 ŷ projw (y) = -22/19 -55/38 ŷ-projw (y) = and x₂= ŷ = projw (y) = 4/45 ŷ projw (y) = -17/45 = -4/9 Select one: O a Oc ○b. J(Y) = O d. J(Y₂) = -1/2 -1 -3/2 Ponsider th Consider the following nonlinear system of differential equations at (x, y) = (1, 0) (which could also be written as a column vector Y₁ = J(Y) = J(Y₂)= 3/19 -3/19 1/19 Note that x, and x₂ are orthogonal and therefore form an orthogonal basis for the (1³) 0 (²) 3 -5 3 (1³) 0 3 -5 -5 What is the orthogonal projection projw (y) of y onto W? N&HE -z + 3y -5y This system has an equilibrium point Which matrix is the Jacobian matrix J(Y)?
ion ion Cet A=( -0.2 -0.3 -0.2 0.3 using the matrix exponential e^ and equals p' (Y₁) = e^Y₁ = (e The eigenvalues of eª end up equaling e 0.210.3 0.782163 ± 0.241951. By what angle, to the nearest tenth of a degree, does the linear transformation p¹: R² → R² rotate points counterclockwise around the origin? Select one: O a. 0 17.2° O b. 0 72.8° Oc. 0≈ 33.7 O d. 0≈ 56.3° Check so that the eigenvalues of A are -0.2 ± 0.3i, where 2-1. The time-1 flow map is defined e-0.2 cos(0.3) -e-02 sin(0.3) e-02 Yo Once you have entered code for NDSolve and stored it in a variable, perhaps called "Solution", or something similar, what Mathematica "operator" (a symbol that "does something") allows you to access the "data" stored in this variable for various purposes (such as graphing approximate solutions of differential equations). Select one: O a. || ("double pipe") O b. /. ("slash dot") O c. //("slash slash") O d. & ("ampersand")
Transcribed Image Text:ion ion Cet A=( -0.2 -0.3 -0.2 0.3 using the matrix exponential e^ and equals p' (Y₁) = e^Y₁ = (e The eigenvalues of eª end up equaling e 0.210.3 0.782163 ± 0.241951. By what angle, to the nearest tenth of a degree, does the linear transformation p¹: R² → R² rotate points counterclockwise around the origin? Select one: O a. 0 17.2° O b. 0 72.8° Oc. 0≈ 33.7 O d. 0≈ 56.3° Check so that the eigenvalues of A are -0.2 ± 0.3i, where 2-1. The time-1 flow map is defined e-0.2 cos(0.3) -e-02 sin(0.3) e-02 Yo Once you have entered code for NDSolve and stored it in a variable, perhaps called "Solution", or something similar, what Mathematica "operator" (a symbol that "does something") allows you to access the "data" stored in this variable for various purposes (such as graphing approximate solutions of differential equations). Select one: O a. || ("double pipe") O b. /. ("slash dot") O c. //("slash slash") O d. & ("ampersand")
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