Answer in following concerning span and linear combinations a) describe circumstance in which the...
answer in following concerning span and linear combinations
a) describe circumstance in which the span vectors {u,v,w} is a plane in R3
b) determine if given vector w is a linear combination of vector v1 = <1,2> and vector v2 = <1,3>. If it is, find a, b such that vector w = aV1 + bV2 (v1,v2 are vectors). Use vector w = <1,-5>
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Answer in following concerning span and linear combinations a) describe circumstance in which the...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector...
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
Mark each statement as True or False and justify your answer. a) The columns of a...
Mark each statement as True or False and justify your answer. a) The columns of a matrix A are linearly independent, if the equation Ax = 0 has the trivial solution. b) If vi, i = 1, ...,5, are in RS and V3 = 0, then {V1, V2, V3, V4, Vs} is linearly dependent. c) If vi, i = 1, 2, 3, are in R3, and if v3 is not a linear combination of vi and v2, then {V1, V2,...
linear alegbra Let u, v, w be linearly independent vectors in R3. Which statement is false?...
linear alegbra
Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2...
Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2 The x-y plane Question 2 2 pts Describe the span of {(1,1,1),(-1,-1, -1), (2,2, 2)} in R3 A plane passing through the origin Aline passing through the origin R3 A plane not passing through the origin A line not passing through the origin Question 3 2 pts Let u and v be vectors in R™ Then U-v=v.u True False Question 4 2 pts Ifu.v...
3. [1 mark each] Determine which of the following statements are true and which are false....
3. [1 mark each] Determine which of the following statements are true and which are false. (a) The inverse of a rotation matrix (Rº) is (R-8). (b) If the vectors V1, V2, ..., Vk are such that no two of these vectors are scalar multiples of each other then they must form a linearly independent set. (c) The set containing just the zero vector, {0}, is a subspace of R”. (d) If v, w E R3 then span(v, w) must...
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given...
please anyone answer all the questions as soon please
2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
Homework: Section 4.1 Score: 0 of 1 pt 4.1.13 3 4 11 Let v1 0 ,...
Homework: Section 4.1 Score: 0 of 1 pt 4.1.13 3 4 11 Let v1 0 , V2|1 V3 3 and w= 1 1 4 10 Is w in {v,, v2, v3}? How many vectors are in {v,, v, V3}? b. How many vectors are in Span{v, V2, V3}? c. Is w in the subspace spanned by (v,, v2, V3)? Why? a a. Is w in {v, V2 V31? O A. Vector w is in {v,, v2, V3} because it is...
Use the following steps to find the general equation of the plane that intersects the surface...
Use the following steps to find the general equation of the plane that intersects the surface f(x, y) ye2x-y+5 at f(-1,3) Choose any vector ū, u # 0, in the xy-plane that is parallel to neither the x-axis nor the y а) axis. Use a cross product to show that u is parallel to neither axis. Find Duf-1,3) b) Choose any vector v, v *0, in the xy-plane that is orthogonal to u. Use the dot product to show that...
Can I get help with questions 2,3,4,6? be the (2) Determine if the following sequences of vectors vi, V2, V3 are linear...
Can I get help with questions 2,3,4,6?
be the (2) Determine if the following sequences of vectors vi, V2, V3 are linearly de- pendent or linearly independent (a) ces of V 0 0 V1= V2 = V3 = w. It (b) contains @0 (S) V1= Vo= Va (c) inations (CE) n m. -2 VI = V2= V3 (3) Consider the vectors 6) () Vo = V3 = in R2. Compute scalars ,2, E3 not all 0 such that I1V1+2V2 +r3V3...
5. [10 points) (a) Determine if the set of all linear combinations of the vectors V1...
5. [10 points) (a) Determine if the set of all linear combinations of the vectors V1 = (1,1,1), V2 = (1,0,1), V3 = (3,2,1) coincides with R. (b) Determine if b= is in the column space of A = 13 1 11 2 0 1 . If yes, write bas a linear 1 1 1] combination of columns of A.
(1) Let u = (-1,2) and v = (3, 1). (a) (5] Find graphically the vector w = (2u - v). (b) (5] Find algebraically the vector z=3u - 2 (2) (a) [5] Write u ='(1, -5, -1) as a linear combination of v1 = (1,2,0), v2 = (0,1,-1), V3 = (2,1,1). (b) (5] Are the 4 vectors u, V1, V2, V3 linearly independent? Explain your answer. (C) (5) Are the 2 vectors V, V3 linearly independent? Explain your answer....
Mark each statement as True or False and justify your answer. a) The columns of a matrix A are linearly independent, if the equation Ax = 0 has the trivial solution. b) If vi, i = 1, ...,5, are in RS and V3 = 0, then {V1, V2, V3, V4, Vs} is linearly dependent. c) If vi, i = 1, 2, 3, are in R3, and if v3 is not a linear combination of vi and v2, then {V1, V2,...
linear alegbra
Let u, v, w be linearly independent vectors in R3. Which statement is false? (A) The vector u+v+2w is in span(u + u, w). (B) The zero vector is in span(u, v, w) (C) The vectors u, v, w span R3. (D) The vector w is in span(u, v).
Question 1 2 pts Describe the span of {(1,0,0),(0,0,1)} in R3 The x-z plane R3 R2 The x-y plane Question 2 2 pts Describe the span of {(1,1,1),(-1,-1, -1), (2,2, 2)} in R3 A plane passing through the origin Aline passing through the origin R3 A plane not passing through the origin A line not passing through the origin Question 3 2 pts Let u and v be vectors in R™ Then U-v=v.u True False Question 4 2 pts Ifu.v...
3. [1 mark each] Determine which of the following statements are true and which are false. (a) The inverse of a rotation matrix (Rº) is (R-8). (b) If the vectors V1, V2, ..., Vk are such that no two of these vectors are scalar multiples of each other then they must form a linearly independent set. (c) The set containing just the zero vector, {0}, is a subspace of R”. (d) If v, w E R3 then span(v, w) must...
please anyone answer all the questions as soon please
2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
Homework: Section 4.1 Score: 0 of 1 pt 4.1.13 3 4 11 Let v1 0 , V2|1 V3 3 and w= 1 1 4 10 Is w in {v,, v2, v3}? How many vectors are in {v,, v, V3}? b. How many vectors are in Span{v, V2, V3}? c. Is w in the subspace spanned by (v,, v2, V3)? Why? a a. Is w in {v, V2 V31? O A. Vector w is in {v,, v2, V3} because it is...
Use the following steps to find the general equation of the plane that intersects the surface f(x, y) ye2x-y+5 at f(-1,3) Choose any vector ū, u # 0, in the xy-plane that is parallel to neither the x-axis nor the y а) axis. Use a cross product to show that u is parallel to neither axis. Find Duf-1,3) b) Choose any vector v, v *0, in the xy-plane that is orthogonal to u. Use the dot product to show that...
Can I get help with questions 2,3,4,6?
be the (2) Determine if the following sequences of vectors vi, V2, V3 are linearly de- pendent or linearly independent (a) ces of V 0 0 V1= V2 = V3 = w. It (b) contains @0 (S) V1= Vo= Va (c) inations (CE) n m. -2 VI = V2= V3 (3) Consider the vectors 6) () Vo = V3 = in R2. Compute scalars ,2, E3 not all 0 such that I1V1+2V2 +r3V3...
5. [10 points) (a) Determine if the set of all linear combinations of the vectors V1 = (1,1,1), V2 = (1,0,1), V3 = (3,2,1) coincides with R. (b) Determine if b= is in the column space of A = 13 1 11 2 0 1 . If yes, write bas a linear 1 1 1] combination of columns of A.
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