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Show that Χ'1) (1) and x(2)(1) are linearly dependent at each point in...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use...
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Show that the matrix is not diagonalizable. 1-42 13 0 02 STEP 1: Use the fact...
Show that the matrix is not diagonalizable. 1-42 13 0 02 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (11.22) = STEP 2: Find the eigenvectors Xi and X2 corresponding to 1, and 12, respectively. X1 = X2 - STEP 3: Since the matrix does not have ---Select-- linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y,x), then find al...
Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y,x), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation. (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V V such that U is not an invariant subspace of f Hence, or otherwise, show that: a vector subspace U-0 or U = V, if and...
Results for this submission Entered Answer Preview linearly dependent linearly dependent 0; 0; 0; 0 0;...
Results for this submission Entered Answer Preview linearly dependent linearly dependent 0; 0; 0; 0 0; 0; 0; 0 At least one of the answers above is NOT correct. -17 | 30 -12 (1 point) Are the vectors 2 linearly independent? -3 -2 1-3] [3] linearly independent If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation...
a brief explanation of each Question 2 | 13 points Show details of your work. [1...
a brief explanation of each
Question 2 | 13 points Show details of your work. [1 -2 0 0 3 [1 0 0 -2 37 2 -5 -3 -2 6 0 1 0 -1 0 Given matrices 0 5 15 100 and 00110 (2 6 18 8 6 0 0 0 0 0 where the matrix R is the reduced echelon form of the matrix A. a) [2 points Find a basis of the Row(A) {{1,0,0,–2,3], [0,1,0, -1,0], [0,0,1,1,0}} b)...
Please do number 2 Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove...
Please do number 2
Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the eigenvalues of A and AT are the same. 2. (2 points) Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R”. Note that this means in this case) that the eigenvectors are distinct and form a base of the space. 3. (1 point) Given that is an eigenvalue...
please help thank you, (1 point) Which of the following sets of vectors are linearly independent?...
please help thank you,
(1 point) Which of the following sets of vectors are linearly independent? A. {( 10, -16), (-5, 8 )} B. {(-4, -7, 1, -8), (1, 3, 9, 7)} c.{(-2, -6)} D.{(1, 3), (-7, 1)} E.{(-9, 4), (0,0)} F.{(0,0)} G.{(-3, 7), (9,-4), (5,-8)} H.{(6, 1, -8), (1, 2, 5)} (1 point) Are the vectors and 10 28 linearly independent? 19 linearly dependent If they are linearly dependent, find scalars that are not all zero such that the...
2 -25 4)[10+10+10pts.) a) Find the eigenvalues and the corresponding eigenvectors of the matrix A =...
2 -25 4)[10+10+10pts.) a) Find the eigenvalues and the corresponding eigenvectors of the matrix A = b) Find the projection of the vector 7 = (1, 3, 5) on the vector i = (2,0,1). c) Determine whether the given set of vectors are linearly independent or linearly dependent in R" i) {(2,-1,5), (1,3,-4), (-3,-9,12) } ii) {(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1) }
Question 2 (1 point) 8 -18 Find the eigenvalues and eigenvectors of the matrix A =...
Question 2 (1 point) 8 -18 Find the eigenvalues and eigenvectors of the matrix A = 18] (The 3 -7 same as in the previous problem.) di = 2, V1 = [1] and 12 = -1, V2 = - [11] [1] 3 21 = 1, V1 = ܒܗ ܟܬ and 12 = -2, V2 = 2 x = 1, V1 = and 12 = -2, V2 = [11 11 x = -2, Vi and 12 = -3, V2 [1]
Problem 2 Determine if the following functions are linearly independent or linearly dependent. If you believe...
Problem 2 Determine if the following functions are linearly independent or linearly dependent. If you believe that they are linearly dependent (i.e. W(5,9) (+) = 0, for all t in some interval) find a dependence relation. 1. f(t) = cost, g(t) = sint 2. f(t) = 61, g(t) = 64+2 3. f(t) = 9 cos 2t, g(t) = 2 cos? t - 2 sinat 4. f(t) = 2t>, g(t) = 14
Show that the matrix is not diagonalizable. 2 43 0 21 0 03 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) -- STEP 2: Find the eigenvectors x, and X corresponding to d, and 12, respectively, STEP 3: Since the matrix does not have Select linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Show that the matrix is not diagonalizable. 1-42 13 0 02 STEP 1: Use the fact that the matrix is triangular to write down the eigenvalues. (Enter your answers from smallest to largest.) (11.22) = STEP 2: Find the eigenvectors Xi and X2 corresponding to 1, and 12, respectively. X1 = X2 - STEP 3: Since the matrix does not have ---Select-- linearly independent eigenvectors, you can conclude that the matrix is not diagonalizable.
Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y,x), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation. (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V V such that U is not an invariant subspace of f Hence, or otherwise, show that: a vector subspace U-0 or U = V, if and...
Results for this submission Entered Answer Preview linearly dependent linearly dependent 0; 0; 0; 0 0; 0; 0; 0 At least one of the answers above is NOT correct. -17 | 30 -12 (1 point) Are the vectors 2 linearly independent? -3 -2 1-3] [3] linearly independent If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation...
a brief explanation of each
Question 2 | 13 points Show details of your work. [1 -2 0 0 3 [1 0 0 -2 37 2 -5 -3 -2 6 0 1 0 -1 0 Given matrices 0 5 15 100 and 00110 (2 6 18 8 6 0 0 0 0 0 where the matrix R is the reduced echelon form of the matrix A. a) [2 points Find a basis of the Row(A) {{1,0,0,–2,3], [0,1,0, -1,0], [0,0,1,1,0}} b)...
Please do number 2
Assume all matricies are Mmxm(R) unless otherwise specified. 1. (1 point) Prove or disprove that the eigenvalues of A and AT are the same. 2. (2 points) Let A be a matrix with m distinct, non-zero, eigenvalues. Prove that the eigenvectors of A are linearly independent and span R”. Note that this means in this case) that the eigenvectors are distinct and form a base of the space. 3. (1 point) Given that is an eigenvalue...
please help thank you,
(1 point) Which of the following sets of vectors are linearly independent? A. {( 10, -16), (-5, 8 )} B. {(-4, -7, 1, -8), (1, 3, 9, 7)} c.{(-2, -6)} D.{(1, 3), (-7, 1)} E.{(-9, 4), (0,0)} F.{(0,0)} G.{(-3, 7), (9,-4), (5,-8)} H.{(6, 1, -8), (1, 2, 5)} (1 point) Are the vectors and 10 28 linearly independent? 19 linearly dependent If they are linearly dependent, find scalars that are not all zero such that the...
2 -25 4)[10+10+10pts.) a) Find the eigenvalues and the corresponding eigenvectors of the matrix A = b) Find the projection of the vector 7 = (1, 3, 5) on the vector i = (2,0,1). c) Determine whether the given set of vectors are linearly independent or linearly dependent in R" i) {(2,-1,5), (1,3,-4), (-3,-9,12) } ii) {(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1) }
Question 2 (1 point) 8 -18 Find the eigenvalues and eigenvectors of the matrix A = 18] (The 3 -7 same as in the previous problem.) di = 2, V1 = [1] and 12 = -1, V2 = - [11] [1] 3 21 = 1, V1 = ܒܗ ܟܬ and 12 = -2, V2 = 2 x = 1, V1 = and 12 = -2, V2 = [11 11 x = -2, Vi and 12 = -3, V2 [1]
Problem 2 Determine if the following functions are linearly independent or linearly dependent. If you believe that they are linearly dependent (i.e. W(5,9) (+) = 0, for all t in some interval) find a dependence relation. 1. f(t) = cost, g(t) = sint 2. f(t) = 61, g(t) = 64+2 3. f(t) = 9 cos 2t, g(t) = 2 cos? t - 2 sinat 4. f(t) = 2t>, g(t) = 14
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