Find the kernel and image of the linear transformation and state whether it is an isomorphism.Remember a linear transformation is an isomorphism if and only if the kernel is trivial (equals the zeroelement only) and the image is everything.T(M) M1 236from R2×2 to R²:x2 x 2

Answered: Find the kernel and image of the linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Determine which of the following are linear transformations from R4 to R³. For any which are not, give a reason why not. For any which are, find the kernel (also known as null space) and image, and verify that the dimension of the kernel plus the dimension of the image is 4: X 3x ~()- () -() 0₁ x + 2y + z (ii) 0₂ 2x+y-z - 2t t t ()-( t (iii) 03 xy xz + 2yt 3xt + 3z - 2z+t 2+y+z+t 2y +7z X-
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let a=(3,4,5), b=(1, -2, 1) c=(-4, 1, 3). Consider the transformation L: R3-R3 defined by L(v)=v-2(v*a/a*a)*a, write a description of the linear transformation L, including the transformation does geometrically.
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Find the kernel and image of the linear transformation and state whether it an isomorphism. Remember a linear transformation is an isomorphism if and only if the kernel is trivial (equals the zero element only) and the image is everything. [1 2] M[1₁²] 3 T(M) = M from R2×2, to R2x2