For each of the following matrices, determine a basis for each of the subspaces R(AT), N(A), R(A), and N(AT): A=begin{bmatrix}3 & 4 6 & 8 end{bmatrix}

Emily-Jane Bray 2021-01-28 Answered
For each of the following matrices, determine a basis for each of the subspaces R(AT), N(A), R(A), and N(AT):
A=[3468]
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Expert Answer

nitruraviX
Answered 2021-01-29 Author has 101 answers

Step 1
Given:
A=[3468]
Step 2
AT=[3648]
Apply R2R243R1
=[3600]
whose rank is 1
R(AT)=(34)
Now, N(AT)
3x+6y=0
x=2y
(xy)=(2yy)
=(21)  [y=1]
N(AT)=(21)
A=[3468]
Apply R2R22R1
[3400]
Whose rank is 1
R(A)=(36)
For N(A)
3x+4y=0
x=43y
Step 3
(xy)=(43yy)
=(431)  [y=1]
N(A)=(431)

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Jeffrey Jordon
Answered 2022-01-30 Author has 2313 answers

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