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question reveal an important connection between linear independence and linear transformations and provide practice
question assume that a is row equivalent to b find bases for nul a and col
question find bases for the null spaces of the matrices given
question determine whether the sets in bases for r3 of the sets that are not bases determine which ones are linearly
question let h span v1 v2 and k span v3 v4 wherethen h and k are subspaces of r3 in fact h and k are planes in r3
question with a as in exercise find a nonzero vector in nul a and a nonzero vector in col aexercise a find k such that
question find an explicit description of nul a by listing vectors that span the null
question a find k such that nul a is a subspace of rk and b find k such that col a is a subspace of
question the set of all continuous real-valued functions defined on a closed interval a b in r is denoted by c a b this
question let w be the set of all vectors of the form shown where a b and c represent arbitrary real numbers in each
question show that w is in the subspace of r4 spanned by v1 v2 v3
question determine if y is in the subspace of r4 spanned by the columns of a
question let j be the n x n matrix of all 1s and consider a a - b i bj that isconfirm that det a a - bn-1 a n - 1b
question determine the area of the parallelogram determined by the points 1 4 1 5 3 9 and 5 8 how can you tell that the
question combine the methods of row reduction and cofactor expansion to compute the determinants
question each equation illustrates a property of determinants state the
question how is det a-1 related to det a experiment with random n x n integer matrices for n 4 5 and 6 and make a
question compute the determinants using a cofactor expansion across the first
question the vector x is in a subspace h with a basis b b1 b2 find the b-coordinate vector of
question display a matrix a and an echelon form of a find bases for col a and nul a and then state the dimensions of
question find a basis for the subspace spanned by the given vectors what is the dimension of the
question construct bases for the column space and the null space of the given matrix a justify your
question display sets in r2 assume the sets include the bounding lines in each case give a specific reason why the set