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MATH 218 TEST 2 Questions And Answers Latest Update $14.99   Add to cart

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MATH 218 TEST 2 Questions And Answers Latest Update

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MATH 218 TEST 2 Questions And Answers Latest Update

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  • November 1, 2024
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  • 2024/2025
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MATH 218 TEST 2 Questions And
Answers Latest Update
what factorization forms a basis for left null space ANS✔✔ EA=R

if A is an mxn matrix with rank r (easily seen wtih R), the last m-r rows of E form basis of left null
space.



how to verify if vector is in column space ANS✔✔ row reduce A augmented with b



if there's no pivot in the augmented column, b belongs to the column space



how to verify if a vector is in the null space ANS✔✔ multiply the matrix by the vector



if the answer is 0 it is in the null space



how to verify vector is in the row space ANS✔✔ augment with the vector and row reduce



if there is no pivot in the augmented column the vector belongs to the row space



how to verify if vector is in the left null space ANS✔✔ check if the transpose of A times the vector
is 0



or



check if the transpose of the vector times A is 0



how to produce vectors in the null space ANS✔✔ augment A with the 0 vector and parametrize.

, 2024/2025


null space is the vectors multiplied by the scalars



same as saying null space is spanned by those vectorsmu



how to produce vectors in the column space ANS✔✔ multiply matrix by any vector x and resulting
matrix is in the column space



how to produce vectors in the row space ANS✔✔ multiply transpose of matrix by any vector x and
resulting matrix is in the row space



basis of null space ANS✔✔ same process as producing vectors in the null space



basis is that span



basis of left null space ANS✔✔ same process as producing vectors in the left null space



basis is that span



basis of column space ANS✔✔ the pivot columns of A



note: though the pivot columns of rref(A) match up, NOT the same entries, so you must have the
matrix A



OR



nonzero row of the rref of the matrix transposed



basis of row space ANS✔✔ the pivot columns of the transpose of A

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