3. Let A be a matrix of a linear transformation p : R³ → R³ with respect to the natural basis. Find a basis of the image and the kernel of p. -() 1 2 3 4 5 6 A = 7 89
3. Let A be a matrix of a linear transformation p : R³ → R³ with respect to the natural basis. Find a basis of the image and the kernel of p. -() 1 2 3 4 5 6 A = 7 89
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 3CM: Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions...
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Step 1
Consider the given matrix as which represents the linear transformation between and .
For the kernel of the linear transformation set , where X is the column vector of the 3 cross 1 order.
Substitute the matrix in the equation .
Step 2
Convert the matrix into row reduced echelon form by the set of row operations as below:
The above row reduced echelon form gives or .
Thus, the basis for the kernel is obtain below:
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