![(2 points) -3-5 9 Let A = 3 6 -12 ,v= 5 , w= 3 and x = 1 |-3-7 15 ] Is v in Nul(A)? Type yes or no. Is w in Nul(A)? Type](http://img.homeworklib.com/questions/93b452c0-f08d-11eb-b2ac-9f347646f4c0.png?x-oss-process=image/resize,w_560)
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Problem 9. (1 point) T -5 10 1 Let A= and w= 2 -4 Is w...
Problem 9. (1 point) T -5 10 1 Let A= and w= 2 -4 Is w in Col(A)? Type "yes" or "no". Is w in Nul(A)? Type "yes" or "no". Note: You can earn partial credit on this problem.
7. Let A be a 5 x 5 matrix such that 1 2 .40 3 3...
7. Let A be a 5 x 5 matrix such that 1 2 .40 3 3 6 0 9 3 • det(A+15) = 0 • Nul(A) is 3 dimensional. (a) (5 points) What is rank(A)? Explain the reason why. (b) (5 points) What are the cigenvalues of A? (c) (5 points) Write down the characteristic polynomial of A. (d) (5 points) Is A diagonalizable? Why or Why not?
(5 points) Let 5 -4 v= 1-3 -3 and let W the subspace of R4 spanned...
(5 points) Let 5 -4 v= 1-3 -3 and let W the subspace of R4 spanned by ū and 7. Find a basis of W?, the orthogonal complement of W in R4.
V W | | Let A-(as)- | ↓ ↓ -5 2. Let v and w -...
V W | | Let A-(as)- | ↓ ↓ -5 2. Let v and w - I be the 3 2 matrix whose columns are v and w and let B - (b; - be the 2 x 3 matrix whose 1 WT → rows are v1 and w1. Find a1, a13, a21, b32, bi2, and b22 if possible
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2...
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2 Find a basis for Col(A) and a basis for Nul(A). Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
Question 3. (20 pts) Let A= -3 9-27 2 -6 48 3 -9 -2 2 Question...
Question 3. (20 pts) Let A= -3 9-27 2 -6 48 3 -9 -2 2 Question 4. (15 pts) Let the matrix A be the same as in Question 3 (1). Find the rank of A (2). Find the dimensions of Nul(A) and (0) (3). How do the dimensions of Nul(A) and Call relate to the mber of columns of A?
2 1 3 4 -2 5 7 -2 9 Problem 9 Let uj = u2 =...
2 1 3 4 -2 5 7 -2 9 Problem 9 Let uj = u2 = 13 2 Also let v= 0 5 3 10 -6 0 11 1 1 7 a) (4 pts) Compute prw(v) where W = Span{u1, U2, U3} CR5. b) [4 pts) Compute prw(v) where w+ denotes the orthogonal complement of W in R5. c) [3 pts) Compute the distance between v and W.
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find...
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
Question 5 True of False part II: 5 problems, 2 points each. (6). Let w be...
Question 5 True of False part II: 5 problems, 2 points each. (6). Let w be the x-y plain of R3, then wlis any line that is orthogonal to w. (Select) (7). Let A be a 3 x 3 non-invertible matrix. If Ahas eigenvalues 1 and 2, then A is diagonalizable. Sele (8). If an x n matrix A is diagonalizable, then n eigenvectors of A form a basis of " [Select] (9). Letzbean x 1 vector. Then all matrices...
h 7. Let A = 134 -1 2 6 6 0 6 3 9 0 9...
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7. Let A = 134 -1 2 6 6 0 6 3 9 0 9 2 -3 -3 0 Find basis for Nul(A) and Col(A). 3 و 3
Problem 9. (1 point) T -5 10 1 Let A= and w= 2 -4 Is w in Col(A)? Type "yes" or "no". Is w in Nul(A)? Type "yes" or "no". Note: You can earn partial credit on this problem.
7. Let A be a 5 x 5 matrix such that 1 2 .40 3 3 6 0 9 3 • det(A+15) = 0 • Nul(A) is 3 dimensional. (a) (5 points) What is rank(A)? Explain the reason why. (b) (5 points) What are the cigenvalues of A? (c) (5 points) Write down the characteristic polynomial of A. (d) (5 points) Is A diagonalizable? Why or Why not?
(5 points) Let 5 -4 v= 1-3 -3 and let W the subspace of R4 spanned by ū and 7. Find a basis of W?, the orthogonal complement of W in R4.
V W | | Let A-(as)- | ↓ ↓ -5 2. Let v and w - I be the 3 2 matrix whose columns are v and w and let B - (b; - be the 2 x 3 matrix whose 1 WT → rows are v1 and w1. Find a1, a13, a21, b32, bi2, and b22 if possible
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2 Find a basis for Col(A) and a basis for Nul(A). Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
Question 3. (20 pts) Let A= -3 9-27 2 -6 48 3 -9 -2 2 Question 4. (15 pts) Let the matrix A be the same as in Question 3 (1). Find the rank of A (2). Find the dimensions of Nul(A) and (0) (3). How do the dimensions of Nul(A) and Call relate to the mber of columns of A?
2 1 3 4 -2 5 7 -2 9 Problem 9 Let uj = u2 = 13 2 Also let v= 0 5 3 10 -6 0 11 1 1 7 a) (4 pts) Compute prw(v) where W = Span{u1, U2, U3} CR5. b) [4 pts) Compute prw(v) where w+ denotes the orthogonal complement of W in R5. c) [3 pts) Compute the distance between v and W.
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
Question 5 True of False part II: 5 problems, 2 points each. (6). Let w be the x-y plain of R3, then wlis any line that is orthogonal to w. (Select) (7). Let A be a 3 x 3 non-invertible matrix. If Ahas eigenvalues 1 and 2, then A is diagonalizable. Sele (8). If an x n matrix A is diagonalizable, then n eigenvectors of A form a basis of " [Select] (9). Letzbean x 1 vector. Then all matrices...
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7. Let A = 134 -1 2 6 6 0 6 3 9 0 9 2 -3 -3 0 Find basis for Nul(A) and Col(A). 3 و 3
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