2023-12-07T17:58:13+03:00[Europe/Moscow] en true <p>Linear eqn form</p>, <p>What is a solution set of linear eqns</p>, <p>What is row equivalence</p>, <p>What happens if two augmented matrices are row equivalent?</p>, <p>How many matrices can one matrix be row equivalent to in RREF</p>, <p>Pivot position/Pivot column</p>, <p>What is a basic and a free variable</p>, <p>What makes a linear system consistent? What is a unique soln? What is infinitely many solutions?</p>, <p>What is a span?</p>, <p>What is an elementary matrix? What is a permuatation matrix?</p>, <p>What is the product of two lower (upper) triangular matrices?</p>, <p>When does a matrix A have an LU-Decomp?</p>, <p>What are the L and U linear systems?</p>, <p>What is a permuation matrix?</p>, <p>What is dot product</p>, <p>The norm of v is</p>, <p>What is pairwise orthogonal?</p>, <p>What makes a subset a subspace?</p>, <p>What makes a span a subspace?</p>, <p>What is a column space?</p>, <p>For linear system Ax = b. Is b in the col(A)?</p>, <p>What is a nullspace?</p>, <p>Is the null space a subspace?</p>, <p>Can a subset be a subspace for a vector space?</p>, <p>What is linearly independence?</p>, <p>What is a basis?</p>, <p>What is a dimension of V?</p>, <p>What does it mean for a basis to be a minimal spanning set?</p>, <p>What is the rank of a matrix?</p>, <p>dimNul(A) if A is M x N</p>, <p>dimCol(A) if A is M x N</p>, <p>What is the col(A^T) and col(B^T) if they are row equivalent?</p>, <p>What do the non-zero rows in an echelon form matrix A form?</p>, <p>What is an orthogonal compliment?</p>, <p>Is Nul(A) an orthogonal compliment of Col(A^T)</p>, <p>How to express a vector w in V(vector space)</p>, <p>Coordinate Vector Definition</p>, <p>What is a standard basis</p>, <p>Change of base matrix</p>, <p>Solving for the original vector (v) if given the basis (B) and the coordinate vector (vB)</p>, <p>Computing </p>, <p>Computing</p>, <p>What is a Orthogonal Basis</p>, <p>Solving for a vector using an orthogonal basis </p>, <p>What makes an N x N matrix orthogonal?</p>, <p>What is a linear transformation?</p>, <p>What values completely determine T if T is a linear transformation? (Where v1,...vn, is a basis of V) (Vector Spaces)</p>, <p>How can we break down the liner transformation T into a matrix A and the standard basis E?</p>, <p>How to change linear transformations into matrix multiplication</p>, <p>How to go from one base to another, change dimensions using a linear transformation then go from that base to another base </p> flashcards

Math 257

Weeks 1-7

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  • Linear eqn form

  • What is a solution set of linear eqns

  • What is row equivalence

    When one matrix can be turned into the other via row opertations

  • What happens if two augmented matrices are row equivalent?

    Then they have the same soln set.

  • How many matrices can one matrix be row equivalent to in RREF

    Only one matrix

  • Pivot position/Pivot column

  • What is a basic and a free variable

  • What makes a linear system consistent? What is a unique soln? What is infinitely many solutions?

  • What is a span?

  • What is an elementary matrix? What is a permuatation matrix?

  • What is the product of two lower (upper) triangular matrices?

    The product is also lower (upper)

  • When does a matrix A have an LU-Decomp?

  • What are the L and U linear systems?

  • What is a permuation matrix?

    Its an elementary matrix comprised of elementary row operations to allow a matrix have an LU- Decomp

  • What is dot product

    v*w = v^T(w)

  • The norm of v is

  • What is pairwise orthogonal?

  • What makes a subset a subspace?

    It must be closed under vector addition and scalar multiplication

  • What makes a span a subspace?

  • What is a column space?

  • For linear system Ax = b. Is b in the col(A)?

    Yes, if the linear system Ax = b has a solution.

  • What is a nullspace?

    The set of all solutions to the linear system Ax = 0

  • Is the null space a subspace?

    Yes, it is a subspace of the # of columns in the matrix.

  • Can a subset be a subspace for a vector space?

    Yes, as long as the subset is closed under vector addition and scalar multiplication

  • What is linearly independence?

  • What is a basis?

  • What is a dimension of V?

    The number of Vectors in a basis of V.

  • What does it mean for a basis to be a minimal spanning set?

    The elements of the basis span(V) but you cannot delete any of these elements.

  • What is the rank of a matrix?

    The number of pivots it has.

  • dimNul(A) if A is M x N

    dimNul(A) = N - r (number of free variables)

  • dimCol(A) if A is M x N

    dimCol(A) = r (# of pivots)

  • What is the col(A^T) and col(B^T) if they are row equivalent?

    col(A^T) = col(B^T)

  • What do the non-zero rows in an echelon form matrix A form?

  • What is an orthogonal compliment?

  • Is Nul(A) an orthogonal compliment of Col(A^T)

  • How to express a vector w in V(vector space)

  • Coordinate Vector Definition

  • What is a standard basis

  • Change of base matrix

  • Solving for the original vector (v) if given the basis (B) and the coordinate vector (vB)

  • Computing

    Computing

  • Computing

    Computing

  • What is a Orthogonal Basis

  • Solving for a vector using an orthogonal basis

  • What makes an N x N matrix orthogonal?

  • What is a linear transformation?

    This shows that you can apply T to v and w first then apply a and b. where a and b are scalars

    This shows that you can apply T to v and w first then apply a and b. where a and b are scalars

  • What values completely determine T if T is a linear transformation? (Where v1,...vn, is a basis of V) (Vector Spaces)

  • How can we break down the liner transformation T into a matrix A and the standard basis E?

  • How to change linear transformations into matrix multiplication

  • How to go from one base to another, change dimensions using a linear transformation then go from that base to another base