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provide a glimpse of some widely used matrix factorizations some of which are discussed later in the textreduced lu
math 54 quiz 10-1 find the set of all x in r2 minimizing ax - bk where2 let h be the subspace of r5 given byfind an
an economy that is divided into three sectors-manufacturing agriculture and services for each unit of output
the consumption matrix c below is based on input-output data for the us economy in 1958 with data for 81 sectors
math 54 quiz 9-1 consider the matrixuse a change of basis to represent a as the composite of a rotation and scaling
the leontief production equation x cx d is usually accompanied by a dual price equationwhere p is a price vector
consider the production model x cx d for an economy with two sectors whereuse an inverse matrix to determine the
math 54 quiz 8-1 consider the matrixfind a basis for the eigenspace with eigenvalue lambda 42 find the characteristic
the consumption matrix c for the us economy in 1972 has the property that every entry in the matrix i - c-1 is nonzero
let c be an n x n consumption matrix whose column sums are less than 1 let x be the production vector that satisfies a
math 54 quiz 7-1 find the dimension of the subspace h sub r4 given by all vectors of the formwhere w x y z are any real
math 54 quiz 6-1 let h be the set of 3 times 3 matrices such that a -at these are called skew-symmetric matrices show
suppose an economy has two sectors goods and services one unit of output from goods requires inputs of 2 unit from
math 54 quiz 5-1 suppose a is a 5 times 7 matrix whose rank is 3 what is the dimension of the null space of a justify
a 2 x 100 data matrix d contains the coordinates of 100 points compute the number of multiplications required to
math 54 quiz 4-1 suppose is the standard matrix for an invertible linear transformation s r2 rarr r2 and is the
show that the transformation in exercise 7 is equivalent to a rotation about the origin followed by a translation by p
a rotation on a computer screen is sometimes implemented as the product of two shear-and-scale transformations which
math 54 quiz 3-1 determine if the columns of the matrix form a linearly independent set2 let tx y 3x 2y x - y show
concern the way in which color is specified for display in computer graphics a color on a computer screen is encoded by
math 54 quiz 2-1 find the general solution of the linear system corresponding to the following augmented matrix2
use matrix multiplication to find the image of the triangle with data matrix d under the transformation that reflects
respond as comprehensively as possible and justify your answersuppose f is a 5 x 5 matrix whose column space is not
math 54 quiz 1-1 assume the following assertions are truethere are courses at berkeleyin every berkeley course there is
find the 3 x 3 matrices that produce the described composite 2d transformations using homogeneous coordinatestranslate