[2] 6. 굿%3D |3 | ; 히1 = |, v2 = 4
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Q: 3. The value of k in the variation models y = kx and y = is called the of
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- (a) find the standard matrix A for the linear transformation T and (b) use A to find the image of the vector v. Use a software program or a graphing utility to verify your result.T(x, y, z) = (x + 2y − 3z, 3x − 5y, y − 3z), v = (3, 13, 4)following linear transformation as a matrix relative to the bases {v1, v2} and {w1, w2}. Please give a numerical answer.Determine if the statements below are True or False.If it’s True, explain why. If it’s False explain why not, or simply give an exampledemonstrating why it’s false If a 2 × 2 matrix A is non-invertible, then the image of the unit square under thelinear transformation TA is a line segment
- Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2... are not vectors but are entries in vectors. T(x1,x2,x3,x4) = (x1+7x2, 0, 3x2+x4, x2−x4) (SEE PICTURE)Quadrilateral ABCD undergoes a transformation about the origin (0,0) and Quadrilateral A′B′C′D′ is obtained. Determine the transformation matrix and parameters of transformation.Find a transformation matrix to rotate a vector in R2 through an angle of 30 degrees. Then use it to rotate the vector (3, 7).
- 2. matrix 1\\ v= langle-9,2 rangle is transformed using the transformation matrix A = [[- 4, 1], [- 1, 2]] What is the resulting vector? Show all your workhint: Recall that the matrix-vector product is a linear operation(a) find the standard matrix A for the linear transformation T, (b) use A to find the image of the vector v, and (c) sketch the graph of v and its image.T is the reflection in the vector w = (3, 1) in R2: T(v) = 2 projwv − v, v = (1, 4).
- Translation: define the matrix for the linear mapping that reflects a planes dots in line 4x+3y=0 Please correctly and handwrittenGiven systema) Obtain a suitable transformation matrix that converts matrix A to Jordan form.b) Using the matrix you have found, obtain the new state model.Find the matrix that produces the rotation. Then find the image of the vector (1, −1, 1).90° about the x-axis