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2.14 Determine if the following DT systems are invertible. If yes, find the inverse systems (i) y[k](k 1)x [k 2]; : - |...
1.30. Determine if each of the following systems is invertible. If it is, construct the inverse...
1.30. Determine if each of the following systems is invertible. If it is, construct the inverse system. If it is not, find two input signals to the system that have the same output. (a) ya)-x(t - 4) (c) y[n] nx[n] (b) y(t) = cos(x(t)] x[n - 11, n z 1 In], (e) yIn]-0, ns-1 (g) y[n] x[1 -n] G) y(t) dxt (1) V(f) = X(20) n 0 (k) vini =lx(n+1],
9. Determine whether the following systems are invertible. If so, find the inverse. If not, find...
9. Determine whether the following systems are invertible. If so, find the inverse. If not, find 2 input signals that produce the same output. (a) yo)r (b) yin]- et-, where a is a real number (c) y(t)-Vx'(t) for real-valued signals x(t) (d) Mn]=x[n] (complex conjugate)
9. Determine whether the following systems are invertible. If so, find the inverse. If not, find...
9. Determine whether the following systems are invertible. If so, find the inverse. If not, find 2 input signals that produce the same output. (a) y)-r (b) yn]-ewl, where a is a real number (c) yt)-vx(t) for real-valued signals x(t) (d) yIn] xIn] (complex conjugate) 10. In most of the book, we will be discussing ways to analyze linear time-invariant (LTI) systems. As we will explore in much more detail later, the response of an LTI system to a particular...
10. Determine the values of k for which the system of linear equations has (i) no solution vector...
10. Determine the values of k for which the system of linear equations has (i) no solution vector, (ii) a unique solution vector, (iii) more than one solution vector (x, y, z): (a) kx+ y+ z= (b) 2x + (k-1)y + (3-k)2-1 2y + (k-3): = 2 x+ky + z = 1 -2y+ x 2x + ky- z =-2 (c) x + 2y + k= 1 (d) -3z =-3
10. Determine the values of k for which the system of...
1. For each of the following systems, (i) determine all critical points, (ii) determine the corresponding...
1. For each of the following systems, (i) determine all critical points, (ii) determine the corresponding linear system near each critical point, and (ii) determine the eigenvalues of each linear system and the corresponding conclusion that can be inferred about the nonlinear system. (a) dz/dt x- - zy, dy/dt 3y- xy-2y (b) dr/dt r2 + y, dy/dt=y-ay
1. Use the method of cylindrical shells to find the volume of the following solids rotation (i) Spin the region bound by y -Vx,y 0, x-1 around the y-axis; (ii) Twist the area bound by x -1+(y-2)2 and...
1. Use the method of cylindrical shells to find the volume of the following solids rotation (i) Spin the region bound by y -Vx,y 0, x-1 around the y-axis; (ii) Twist the area bound by x -1+(y-2)2 andx- 2 about the x-axis; (iii) Rotate the region between y - x2 and y -6x-2x2 around the y-axis; (iv) Twirl the space between y V and x 2y about the line x 5 2. Use both methods discussed in class to compute...
Signal system question. EEGR 221 Signals and Systems Homework 3 Determine whether the following systems are...
Signal system question.
EEGR 221 Signals and Systems Homework 3 Determine whether the following systems are (i) Memoryless (ii) Invertible (ii) Casual (iv) Stable (v) Time invariant (vi) Linear (a) y(t)-5x(2t +4) (b) y(t)-7 x(2t 1) +3 (c) y(t)e4x(c) (d) y(t)-sin (x(t + 1)) (e) y(t) x(t)l (1) y() log(x(t)) Your answer must have 3 components for each property 1) Definition of the property 2) Yes or NO 3) Justification and the test that you have done to give the...
Linear Algebra 1) For each of the following linear systems of equations I. 2x, x 3...
Linear Algebra
1) For each of the following linear systems of equations I. 2x, x 3 x,-4x2 = 4 3x, +2x-5 2x, + 3x2-6x3 x 3x2 + 2x 2 -x,-4x2 + 6x3 =-1 III. 5x1 + 7x2=-5 8x1-5x2 = 3 IV, 2 a. Identify corresponding linear algebra nomenclature (4x -b) b. Calculate the inverse of the coefficient matrix (4) for each system Calculate each by hand and check your results with an alternate hand calculation or alternatively through an suitable...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
-trix Example 1: Solve the following systems by finding the inverse of AT 13x+y = 3...
-trix Example 1: Solve the following systems by finding the inverse of AT 13x+y = 3 ems by finding the inverse of the coefficient matrix. [21] B[] cx[j] ab 2 lil (x-2y=8 A -1 Find Al=ad.bc = 1(1) - 1(2) = -1 to 2 x + y = 1 12x + y = 3 A TAL- Z1J IN X=-4+3 x -y=1 sx+y=3 TGA 16-17 -11-25 -110/= 9. x - y = 1 X = A B - 27- 177 2...
1.30. Determine if each of the following systems is invertible. If it is, construct the inverse system. If it is not, find two input signals to the system that have the same output. (a) ya)-x(t - 4) (c) y[n] nx[n] (b) y(t) = cos(x(t)] x[n - 11, n z 1 In], (e) yIn]-0, ns-1 (g) y[n] x[1 -n] G) y(t) dxt (1) V(f) = X(20) n 0 (k) vini =lx(n+1],
9. Determine whether the following systems are invertible. If so, find the inverse. If not, find 2 input signals that produce the same output. (a) yo)r (b) yin]- et-, where a is a real number (c) y(t)-Vx'(t) for real-valued signals x(t) (d) Mn]=x[n] (complex conjugate)
9. Determine whether the following systems are invertible. If so, find the inverse. If not, find 2 input signals that produce the same output. (a) y)-r (b) yn]-ewl, where a is a real number (c) yt)-vx(t) for real-valued signals x(t) (d) yIn] xIn] (complex conjugate) 10. In most of the book, we will be discussing ways to analyze linear time-invariant (LTI) systems. As we will explore in much more detail later, the response of an LTI system to a particular...
10. Determine the values of k for which the system of linear equations has (i) no solution vector, (ii) a unique solution vector, (iii) more than one solution vector (x, y, z): (a) kx+ y+ z= (b) 2x + (k-1)y + (3-k)2-1 2y + (k-3): = 2 x+ky + z = 1 -2y+ x 2x + ky- z =-2 (c) x + 2y + k= 1 (d) -3z =-3
10. Determine the values of k for which the system of...
1. For each of the following systems, (i) determine all critical points, (ii) determine the corresponding linear system near each critical point, and (ii) determine the eigenvalues of each linear system and the corresponding conclusion that can be inferred about the nonlinear system. (a) dz/dt x- - zy, dy/dt 3y- xy-2y (b) dr/dt r2 + y, dy/dt=y-ay
1. Use the method of cylindrical shells to find the volume of the following solids rotation (i) Spin the region bound by y -Vx,y 0, x-1 around the y-axis; (ii) Twist the area bound by x -1+(y-2)2 andx- 2 about the x-axis; (iii) Rotate the region between y - x2 and y -6x-2x2 around the y-axis; (iv) Twirl the space between y V and x 2y about the line x 5 2. Use both methods discussed in class to compute...
Signal system question.
EEGR 221 Signals and Systems Homework 3 Determine whether the following systems are (i) Memoryless (ii) Invertible (ii) Casual (iv) Stable (v) Time invariant (vi) Linear (a) y(t)-5x(2t +4) (b) y(t)-7 x(2t 1) +3 (c) y(t)e4x(c) (d) y(t)-sin (x(t + 1)) (e) y(t) x(t)l (1) y() log(x(t)) Your answer must have 3 components for each property 1) Definition of the property 2) Yes or NO 3) Justification and the test that you have done to give the...
Linear Algebra
1) For each of the following linear systems of equations I. 2x, x 3 x,-4x2 = 4 3x, +2x-5 2x, + 3x2-6x3 x 3x2 + 2x 2 -x,-4x2 + 6x3 =-1 III. 5x1 + 7x2=-5 8x1-5x2 = 3 IV, 2 a. Identify corresponding linear algebra nomenclature (4x -b) b. Calculate the inverse of the coefficient matrix (4) for each system Calculate each by hand and check your results with an alternate hand calculation or alternatively through an suitable...
1. (20 marks) This question is about the system of differential equations Y. dt=(k 1 (a) Consider the case k = 0. i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). ii. Write down the general solution. iii. Sketch a phase portrait for the system. (b) Now consider the case k3 In this case, the matrix has an eigenvalue 2+V/2 with eigenvector i. -1+iv2 and an eigenvalue 2 iv2 with eigenvector . Determine the type of equilibrium...
-trix Example 1: Solve the following systems by finding the inverse of AT 13x+y = 3 ems by finding the inverse of the coefficient matrix. [21] B[] cx[j] ab 2 lil (x-2y=8 A -1 Find Al=ad.bc = 1(1) - 1(2) = -1 to 2 x + y = 1 12x + y = 3 A TAL- Z1J IN X=-4+3 x -y=1 sx+y=3 TGA 16-17 -11-25 -110/= 9. x - y = 1 X = A B - 27- 177 2...
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