Chapter 6: Q 6.2-57E (page 292)
Therefore, the matrix Min terms of A1 and A2 is given by, A1M = -A2.
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for all matricesA andB.
Is the determinant of the matrix
positive or negative? How can you tell? Do not use technology.
The matrix is invertible for all positive constantsk.
In Exercises 5 through 40, find the matrix of the given linear transformation with respect to the given basis. If no basis is specified, use standard basis:for,
forandfor,.For the spaceof upper triangularmatrices, use the basis
Unless another basis is given. In each case, determine whetheris an isomorphism. Ifisn’t an isomorphism, find bases of the kernel and image ofand thus determine the rank of.
21. from to with respect to the basis.
Question: Arguing geometrically, determine whether the following orthogonal transformations frompreserve or reverse orientation. See Exercise 20.
a. Reflection about a plane
b. Reflection about a line
c. Reflection about the origin
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