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Chapter 6: Q26E (page 307)
Consider an nxn matrix A with integer entries such that A=1. Are the entries of necessarily integers? Explain.
Yes, the entries ofis the necessarily integers.
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Find the determinants of the linear transformations in Exercises 17 through 28.
27. , where a and b are arbitrary constants, from the space V spanned by and to V
Use Cramer's rule to solve the systems in Exercises 22 through 24.
23.
(For those who have studied multivariable calculus.) Let Tbe an invertible linear transformation fromto, represented by the matrix M. Letbe the unit square in andits image under T . Consider a continuous functionfromto, and define the function. What is the relationship between the following two double integrals?
and
Your answer will involve the matrix M. Hint: What happens when, for all?
for all matricesA.
Use Gaussian elimination to find the determinant of the matrices A in Exercises 1 through 10.
7.
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