How to: Cofactor expansion 1)pick the row or column with the most zeros 2)Numbers in that row are each of the a's before each cofactor 3)Plus, minus as a checker board Cannot be determined All of the above None of the above

1)pick the row or column with the most zeros 2)Numbers in that row are each of the a's before each cofactor 3)Plus, minus as a checker board

How to: Determinant and row operationEvaluate the determinant of the matrix by first reducing the matrix to ref form. 1)Use row operations to reduce matrix to upper triangular form 2)Take the product of the main diagonal to get determinent None of the above Cannot be determined All of the above

1)Use row operations to reduce matrix to upper triangular form 2)Take the product of the main diagonal to get determinent

How to: Cramers rule All of the above None of the above Cannot be determined 1)Set equations as matrix Ax=b 2)Solve for det(A) 3)Solve for det(A1) replacing first column with b 4)Solve for det(A2) replacing second column with b 5)Find x1 and x2

1)Set equations as matrix Ax=b 2)Solve for det(A) 3)Solve for det(A1) replacing first column with b 4)Solve for det(A2) replacing second column with b 5)Find x1 and x2

How to: Show that Scalars in linear combination do not exist None of the above If there is a row of zeros and c≠0, scalars do not exist All of the above Cannot be determined

If there is a row of zeros and c≠0, scalars do not exist

When do vectors lie on the same plane? All of the above None of the above If vector w is formed by the plane of u+v, w is on that plane. Cannot be determined

If vector w is formed by the plane of u+v, w is on that plane.

Given ||v|| and ||w||, what are the largest and small values possible for ||v-w||? 1)Largest: add to each other if parallel 2)Smallest: subtract from each other if parallel None of the above Cannot be determined All of the above

1)Largest: add to each other if parallel 2)Smallest: subtract from each other if parallel

How to: Vertices of a right triangle from points None of the above 1)Points -> Vectors 2)Check if orthogonal 3)If so, forms a right triangle All of the above Cannot be determined

1)Points -> Vectors 2)Check if orthogonal 3)If so, forms a right triangle

How to: Express the vector as a linear combination of u, v, and w None of the above Cannot be determined All of the above 1)Set up as a linear combination 2)Set up as matrix 3)rref 4)a, b, c values= a1 a2 a3

1)Set up as a linear combination 2)Set up as matrix 3)rref 4)a, b, c values= a1 a2 a3

How to: Determine wither the set {TA(u1) TA(u2) TA(u3)} spans Rn None of the above Cannot be determined 1) Multiply each u by A to find TA(u) 2)Form nxn with TA(u)s 3)Check invertibility using the det(A) 4)If not 0, it spans All of the above

1) Multiply each u by A to find TA(u) 2)Form nxn with TA(u)s 3)Check invertibility using the det(A) 4)If not 0, it spans

Linear Algebra: Cramer's Rule, Basis, Subspaces & Determinants Flashcards

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Algebra - Linear Algebra

user_hassanuml Created by 9 mon ago

Cards in this deck(19)

How to: Cofactor expansion

How to: Determinant and row operationEvaluate the determinant of the matrix by first reducing the matrix to ref form.

How to: Cramers rule

How to: Determinant given dimension=n and det(A)=#

How to: Show that Scalars in linear combination do not exist

When do vectors lie on the same plane?

Given ||v|| and ||w||, what are the largest and small values possible for ||v-w||?

How to: Vertices of a right triangle from points

How to: Express the vector as a linear combination of u, v, and w

How to: Determine wither the set {TA(u1) TA(u2) TA(u3)} spans Rn

How to: Determining whether a set is linearly independent

How to: Show/check set is a Basis for ___

How to: Express Basis as coordinate vector and as a linear combination

How to: given u, Find the coordinate vector of TA(u) related to the basis S={(s1,s2,s3), (v1,v2,v3), (w1,w2,w3) for Rn/

How to: Find the standard basis vector for Rn that can be added to the set {v1 v2} to provide basis for Rn

How to: Find the dimension of the subspace R4 consisting of all vectors x for which TA(x)=0

Change of basis

How to: If B1 and B2 and B3 are bases for R2 and if B1->B2 and PB2->B3, B3->B1?

How to: If the Matrix A is the transition matrix, from what basis B goes to the basis {(u) (v) (w)}?

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Linear Algebra: Cramer's Rule, Basis, Subspaces & Determinants Flashcards

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