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Exercise 1. ( 3 A = 4 - 1 ) (1) Compute the eigenvalue...

Exercise 1. ( 3 A = 4 - 1 ) (1) Compute the eigenvalues of A and draw the eigenspaces of A in the xy plane. (2) Is the matrix A diagonalizable? Explain why. (3) Compute the angle between the eigenspaces of A. (4) Is it possible to find an orthonormal basis of eigenvectors of A? Explain t...

PROBLEM #2 (16 marks) Consider the following matrices. 1 2...

PROBLEM #2 (16 marks) Consider the following matrices. 1 2 1 W 2 - 1 0 4 B = 2 3 1 3 C = 0 - 1 D= W 9 W F = 1 2 3 2 - 5 1 W 3 (a) Compute FC-2B-¹ - . (b) For what value(s) of W is matrix D singular? (c) Assume that M, N and X are all invertible matrices of the same size and that...

4. Use an inverse matrix to solve the equation for X: 5 4 ...

4. Use an inverse matrix to solve the equation for X: 5 4 7 X = 0 1 1 -1 0 1 5. For each of the following, give an example or explain why no example exists (a) The standard matrix A for an onto linear transformation T: IR³ R² (b) A 2 X 3 matrix A such that the linear transformation ...

Q.1 (20) Concepts and vocabulary. Circle "True&...

Q.1 (20) Concepts and vocabulary. Circle "True" or "False". If you choose "False", give reasons or a counter example to support your answer. 1. If A and B are n X n matrices, then (A + B) (A - B) = A²-B². = - (True or False) 2. If A ...

Find the average rate of change of the function f(x) = x&sup...

Find the average rate of change of the function f(x) = x² + 6x from x1 = 1 to x2 2. Find the average rate of change of the function f(x) = 2x from x =0 to x2 = 5. The average rate of change is (Simplify your answer.) Write an equation for line L in point-slope form and slope-intercept form....

Use the graphs of f and g to evaluate the composite function...

Use the graphs of f and g to evaluate the composite function. (f o g)(2) = (f ogg(2) e 10- y=f(x) 8- 6- 2- x 10 -8 -6 -4 s 2 4 6 8 10 g(x) 4- -6- -8- 10 Use the graphs of f and g to find (fg)(0). (fg)(0) = Ay + 6- 4- 2- x 6 5 -3 2 -1 3 4 5 6 -2- f(x) -4- ...

If the system a does have a unique solution for given valu...

If the system a does have a unique solution for given value of a, then that solution is given by x(a;u,v) y(a;u,v) where O 4a-6 4a-6 x(a;u,v) - and y(a;u,v) = 2v-3u v-3au o x(a;u,v) = and y(a;u,v) = 3u-4v av-3u 2a-3 2a-3 o 2u-v av-3u x(a;u,v) = and y(a;u,v) = 2a 3 4a-6 o 2v-5...

PROBLEM #4 (4 marks) TRUE OR FALSE? State whether the follo...

PROBLEM #4 (4 marks) TRUE OR FALSE? State whether the following are TRUE or FALSE. If the statement is true, simply state it is true. If it is false, explain why or give an example that shows it is false. (a) If the number of unknowns in a linear system exceeds the number of equations, then the s...

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