-P3. Let A =31]2-1 313-2 1and B = -2 2 1 0-1 2 0 1Determine a single matrix which inducesthe same transformation as the composite transformation of TB and then TA. Show atransformation diagram which shows the relationships between the domains and co-domainsof TB, TA, and TA TB, including their dimensionality.O

Answered: Image /qna-images/answer/b5d45195-d70b-4d4d-a7b3-a6c0a733ad41.jpg

Answered: -P 3. Let A = 31 2 -1 3 3 -2 1 and B-22…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 77E: Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and...

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Similar questions

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.
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
Let TA: 23 be the matrix transformation corresponding to A=[311124]. Find TA(u) and TA(v), where u=[12] v=[32].
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?
1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .
In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB, where B is a fixed nn matrix
Let T be a linear transformation from M2,2 into M2,2 such that T([1000])=[1102], T([0100])=[0211], T([0010])=[1201],T([0001])=[3110]. Find T([1314]).
Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.

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