Let S be the parallelogram then determine the area of parallelogram by the vectors [h and b2 h/2 [1 and let A = h = 0 h+1 h=102 Also compute the area of the image of parallelogram under the linear transformation "“T"

Q: The line segnment from 0 to a vector u is the set of points of the form tu, where 0SIS1. Show that a…

A: Given that the line segment from 0 to a vector “u” is the set of the form “tu” So, assume that, x =…

Q: 9. If three planes intersect in a point then the triple scalar product (a x b) · c of their normals…

A: As per bartleby policy we are not supposed  to answer  more than one question per post. This post…

Q: Find the bilinear transformation which maps the points (00, i, 0)in the z - plane into (-1, -i, 1)in…

A:

Q: Find a vector a with representation given by the directed line segment AB. A(0, 4, 2), B(4, 4, –1)…

A: Given vectors

Q: Given ABCD and its image EFGH in the plane, which type of transformation has taken place?

A: There are many different rules that are used to transform a figure into another figure. We an…

Q: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

A:

Q: Find a vector a with representation given by the directed line segment E A(0, 3, 2), B(5,3, -5) Draw…

A: We need to find the equation from A(0, 3, 2) and B(5, 3, -5).

Q: Which of the following cannot be defined as an inner product between two vectors (x0, Yo) and (¤1,…

A:

Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: Find the bilinear transformation which maps the points (00, i, 0)in the z - plane into (-1.-1,1)in…

A:

Q: Find the orthogonal projection of y onto Span{u1,u2}. Where, y=(1,1,0,0)*, u1=(1,0,1,0)t…

A:

Q: . Find the image of the line that passes through the point (1, 1) and is parallel to the under the…

A: Here is the solution of the given problem.

Q: Find the bilinear transformation which transform the points (∞,i,0) in the z-plane into the points…

A: We have to find the bilinear transformation which transform the points (∞,i,0) in the z-plane into…

Q: Find the Bilinear Transformation that maps the points (0, 1, ) in z-plane onto the points (-1,-2,-i)…

A:

Q: Under the transformation w = z² obtain the map in the w-plane of the square with vertices (0,0),…

A: The given problem is to find out the region of mapping in w-plane for the transformation w=z2 where…

Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'v' where needed to give…

A:

Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

A: Solution

Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

A:

Q: find the projection of u along v u = (2, 5), v = (1, 1)

A: u=2,5 and v=1,1

Q: Find the bilinear transformation that maps the point (0,1,π=∞) in z-plane onto the point…

A:

Q: 5. Consider a linear transformation T R-R2 which reflects a vector about the line y=-r, and dilates…

A: Consider the given information:

Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

A: Given that V be a finite dimensional vector space with dimension ≥1 and T: V→V be a linear…

Q: The line segment from 0 to a vector u is the set of points of the form tu, where Osis1. Show that a…

A:

Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

A:

Q: find the projection of u along v  u = (1, 1, 1), v = (1, 1, 0)

A: the given vectors are: u=1,1,1v=1,1,0 we have to find the projection of u along v.

Q: Find the projection of u along v. u =〈2, -3〉, v =〈1, 2〉

A: Given: u =〈2, -3〉, v =〈1, 2〉 To find the projection of u along v

Q: EN Find the vector projection of uzbi+3j+2k onto vzi-zj-2k and the scalar component of u in the…

A: The distance we travel in the direction of vector v→, while traversing u→ is called the component of…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, 1, –-2), (2, 3, 4) is O O O O

A: I have append the formula in solution part

Q: Find the scalar and vector projections of b onto a. = (3, –6, –2), b = (3, 3, 2) a

A:

Q: Find the scalar and vector projections of b onto a, where a = (-1,1,2) and b = (-4,5,8).

A: The solution of the problem is given in the next step.

Q: Find the scalar and vector projections of d = (4, 2, –5) on b = (3, –1, 6).

A:

Q: Consider R' endowed with the dot product. Let W = span{u1, u2} where u1 = (1,0, 1) and u2 = (-1, 1,…

A:

Q: Find the bilinear transformation which maps the points (∞,i,0) in the z-plane into (-1,-i,1) in the…

A: Explanation of the solution is given below...

Q: Determine with the properties whether the function is a linear transformation, if not justify your…

A: Since you have asked a question with multiple subparts so as per guidelines we will solve the first…

Q: (4 Let T: R?R² be a linear transformation that first reflects vectors abaut y. axis and then rotates…

A:

Q: Take a defineal a transformation. by OIYE Vectors in the w(x)- cCKed where c and d EU clidean plane…

A: In euclidean plane, d(x,y) = |x-y| ∀x,y∈ℝ.

Q: Let T: RR² be a linear transformation that sends the vector u= (5,2) into (2, 1) and maps v= (1,3)…

A:

Q: Prove Theorem .Let Q be an orthogonalmatrix. detQ=+-1

A: Given that, “Q” be an orthogonal matrix, So, QQT=I=QTQ…

Q: Compute the orthogonal projection of u = form, not a decimal approximation. onto v= 3 2 Leave your…

A: To compute the orthogonal projection of u=-4-89 onto v=132.

Q: Find a basis for the set of vectors in R^3 in the plane 3x - 2y + z = 0. Also state the dimension.

A:

Q: Prove that any linear transformation T : R" → R" maps a line passing through the origin to either…

A: Given: Demonstrate that every linear transformation T: ℝn → ℝn transfers a line through the origin…

Q: Use matrices to transform the vector .3 by a reflection across the x-axis, a horizontal compression…

A: Given:     Vector : ⟨ 7 , 3 ⟩     Reflection across x - axis   Horizontal compression = 1/2…

Q: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

A:

Q: Find the bilinear transformation which transform the point (∞,i,0) in the z-plane into the points…

A:

Q: Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)

A:

Q: Show the Horizontal shear transformation for geometric figures by a 2x2 matrix ?

A:

Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned the…

A: Observe that the parallelogram is spanned by the vectors. <-8,9> and <7,2>

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1,-2), (2,3, 4) is O O O O

A: