Get help now
  • Pages 3
  • Words 685
  • Views 282
  • Download

    Cite

    Clare
    Verified writer
    Rating
    • rating star
    • rating star
    • rating star
    • rating star
    • rating star
    • 4.7/5
    Delivery result 3 hours
    Customers reviews 346
    Hire Writer
    +123 relevant experts are online

    Linear algebra test true and false

    Academic anxiety?

    Get original paper in 3 hours and nail the task

    Get help now

    124 experts online

    a homogeneous equation is always consistent
    TRUE Ax=b always has “trivial” solution (where all the variables are 0)
    the homogeneous equation Ax=0 has the trivial solution if and only if the equation has at least one free variable
    FALSE Ax=0 always has the trivial solution
    the equation Ax=0 gives an explicit description of its solution set
    FALSE the original equation is the implicit description and the explicit description is the equation solved for the span
    the equation x=p + tv describes a line through v parallel to p
    FALSE describes a line through p parallel to v
    a homogeneous system of equations can be inconsistent
    FALSE always has to have one solution x=0
    if x is a nontrivial solution of Ax=0, then every entry in x is nonzero
    FALSE, can have some 0 entries where x=0 but not all
    the equation Ax=b is a homogeneous if the zero vector is a solution
    TRUE the zero vector is always a solution to homogeneous systems
    the columns of A are linearly independent if the equation Ax=0 has the trivial solution
    FALSE a homogeneous system always has the trivial solution
    if S is a linearly dependent set, then each vector is a linear combination of the other vectors S
    FALSE not every vector in a linearly dependent set is a combination of the preceding vectors
    the columns of any 4×5 matrix are linearly dependent
    TRUE is there are more columns than rows then its linearly dependent
    if x and y are linearly independent, and if {x, y, z} is linearly dependent, then z is in Span {x,y}
    TRUE {x, y, z} will be linearly dependent if and only if w is on the plane spanned by u and v
    if u and v are linearly independent, and if w is in the span {u, v}, then {u, v, w} is linearly dependent
    TRUE S={v1…vp} of 2 or more vectors is linearly dependent if and only if at least one of the vectors in S is a linear combination of the others
    if three vectors in R3 lie in the same plane in R3, then they are linearly dependent
    TRUE the third vector must be a multiple of the first or the second vector (who can’t be multiples of each other which means they are linearly independent)
    if a set contains fewer vectors than there are entries in the vectors, then the set is linearly independent
    FALSE set consisting of

    v1=[1, -2, 3] v2= [2, -4, 6]

    is linearly dependent, the theorem p>n does not apply when p

    if a set in Rn is linearly dependent, then the set contains more than n vectors
    FALSE can have the same number of vectors as n
    v1= [3, 1] v2=[6, 2]
    v2 is a multiple of v1 so {v1, v2} is linearly dependent and has the same number of vectors
    if v1…v4 are in R4 and v3=2v1+v2 then {v1, v2, v3, v4} is linearly dependent
    TRUE S={v1…vp} of 2 or more vectors is linearly dependent if and only if at least one of the vectors in S is a linear combination of the others
    if v1 and v2 are in R4 and v2 is not a scalar multiple of v1, then {v1,v2} is linearly dependent
    FALSE the vector v1 could be the zero vector
    if v1,…v5 are in R5 and v3=0 then {v1, v2, v3, v4, v5} is linearly dependent
    TRUE if a set S={v1…vp} in Rn contains the zero vector, then the set is linearly dependent
    if v1, v2, v3 are in R3 and v3 is not a linear combination of v1, v2 then {v1, v2, v3} is linearly independent
    FALSE v1 and v2 can be multiples of each other making the system linearly dependent
    if v1…v4 is in R4 and {v1,v2,v3} is linearly dependent, then {v1, v2, v3, v4} is also linearly dependent
    TRUE a linear dependence relation among v1, v2, v3 may be extended to linear dependence relation among v1, v2, v3, v4 by placing a zero weight on v4
    if {v1…v4} is a linearly independent set of vectors in R4 then {v1, v2, v3} is also linearly independent [think about x1v1+x2v2+x3v3+0*v4=0]
    TRUE if the equation x1v1+x2v2+x3v3+0 x v4=0 had a normal solution with at least one of the other three vectors being nonzero, then so would the equation x1v1+x2v2+x3v3+0 x v4=0. but that cannot happen because {v1, v2, v3, v4} is linearly independent. so {v1, v2, v3} must be linearly independent.
    a linear transformation is a special type of function
    TRUE a linear transformation is a function with certain properties
    if A is a 3 x 5 matrix and T is a transformation defined by T(x)=Ax then the domain of T is R3
    FALSE the domain is R5, the domain of T is the number of columns
    if A is an m x n matrix, then the range of the transformation x |–> Ax is Rm
    FALSE the range is the set of all linear combinations of the columns of A, because each image T(x) is of the form Ax
    every linear transformation is a matrix transformation
    FALSE every matrix transformation is a linear transformation, but not the reverse
    a transformation T is linear if and only if T(c1v1+c2v2)=c1T(v1)+c2T(v2) for all v1 and v2 in the domain of T and for all scalars c1 and c2
    TRUE linear transformations preserve the operations of vector addition and scalar multiplication
    the range of the transformation x |–> Ax is the set of all linear combinations of the columns of A
    TRUE the range is the set of all linear combinations of the columns of A, because each image T(x) is of the form Ax
    every matrix transformation is a linear transformation
    TRUE every matrix transformation is a linear transformation, but not the reverse
    if T: Rn –> Rm is a linear transformation and if c is in Rm, then a uniqueness question is “Is c in the range of T?”
    FALSE this is an existence question, another way of asking if Ax=C is consistent
    A linear transformation preserves the operations of vector addition and scalar multiplication
    TRUE linear transformations preserve the operations of vector addition and scalar multiplication
    a linear transformation T: Rn –> Rm always maps the origin of Rn to the origin of Rm
    TRUE If T is a linear transformation then T(0)=0, and T(cu+dv)=cT(u)+dT(v)

    This essay was written by a fellow student. You may use it as a guide or sample for writing your own paper, but remember to cite it correctly. Don’t submit it as your own as it will be considered plagiarism.

    Need custom essay sample written special for your assignment?

    Choose skilled expert on your subject and get original paper with free plagiarism report

    Order custom paper Without paying upfront

    Linear algebra test true and false. (2018, Oct 20). Retrieved from https://happyessays.com/linear-algebra-test-true-and-false/

    Hi, my name is Amy 👋

    In case you can't find a relevant example, our professional writers are ready to help you write a unique paper. Just talk to our smart assistant Amy and she'll connect you with the best match.

    Get help with your paper
    We use cookies to give you the best experience possible. By continuing we’ll assume you’re on board with our cookie policy