The linear transformation f : R² → R² associated to the matrix1. a rotation by an angle π/2 around the origin2. a rotation by an angle around the origin3. a rotation by an angle 3π/2 around the origin4. some other rotation5. a reflection in the x-axis6. a reflection in the y-axis7. a reflection in some other line.8. a transformation mapping R2 into a line-1 0x (1¹1) is9. none of the above.

The linear transformation f:R2→R2 associated to the matrix -100-1 To find the geometric point of…

Answered: is The linear transformation f : R² →…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 12CM

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Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.
a Let T=[3001]. What effect does T have on the gray square in Table 1? b Let S=[1002]. What effect does S have on the gray square in Table 1? c Apply S to the vertices of the square, and then apply T to the result. What is the effect of the combined transformation? d Find the product matrix W=TS. e Apply the transformation W to the square. Compare to you final result in part c. What do you notice?
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.
Let T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.
The gray square in Table 1 has the following vertices: [00],[10],[11],[01] Apply each of the three transformations given in Table 1 to these vertices and sketch the result to verify that each transformation has the indicated effect. Use c=2 in the expansion matrix and c=1 in the shear matrix.
Here is a data matrix for a line drawing: D=[012100002440] aDraw the image represented by D. bLet T=[1101]. Calculate the matrix product TD, and draw the image represented by this product. What is the effect of the transformation T? cExpress T as a product of a shear matrix and a reflection matrix. See Problem 2. 2. Verify that multiplication by the given matrix has the indicated effect when applied to the gray square in the table. Use c=3 in the expansion matrix and c=1 in the shear matrix. T1=[1001] Reflection in yaxis T2=[100c] Expansion or contraction in ydirection T3=[10c1] Shear in ydirection
For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the preimage of (0,0). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformations T:RnRm by T(v)=Av. Find the dimensions of Rn andRm. A=[0110]
Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is rotation by 5/4π. A = ?
The matrix for a one-to-one linear transformation from \R^4 to \R^3.
The matrix M represents a linear transformation of two-dimensional space and det(M) = 2. What can be said about the area of a region in the plane compared to the area that it is sent to under the transformation? The area of the region is one-half as large.The area of the region is one-third as large. The area of the region triples.The area of the region doubles. The linear transformation T sends all of three-dimensional space to a line. What can you say about the value of the determinant of the matrix representing the transformation? The determinant is negative.The determinant is 0. The absolute value of the determinant is less than 1.

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