Calculus for Business Economics Life Sciences and Social Sciences Plus NEW
13th Edition
ISBN: 9780321925138
Author: Raymond Barnett
Publisher: PEARSON
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Chapter A.6, Problem 94E
In Problems 89–94, evaluate using a calculator. (Refer to the instruction book for your calculator to see how exponential forms are evaluated.)
94.
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Question 4
(a) The following matrices represent linear maps on R² with respect to an
orthonormal basis:
=
[1/√5 2/√5
[2/√5 -1/√5]
"
[1/√5 2/√5]
A =
B =
[2/√5 1/√5] 1
C =
D =
=
=
[ 1/3/5 2/35]
1/√5 2/√5
-2/√5 1/√5'
For each of the matrices A, B, C, D, state whether it represents a self-adjoint
linear map, an orthogonal linear map, both, or neither.
(b) For the quadratic form
q(x, y, z) = y² + 2xy +2yz
over R, write down a linear change of variables to u, v, w such that q in these
terms is in canonical form for Sylvester's Law of Inertia.
[6]
[4]
part b please
Question 5
(a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the
matrix
a cl
|df
equals 3 and the determinant of
determinant of the matrix
a+3b cl
d+3e f
ГЪ
e
[ c ] equals 2. Compute the
[5]
(b) Calculate the adjugate Adj (A) of the 2 × 2 matrix
[1 2
A
=
over R.
(c) Working over the field F3 with 3 elements, use row and column operations to put
the matrix
[6]
0123]
A
=
3210
into canonical form for equivalence and write down the canonical form. What is
the rank of A as a matrix over F3?
4
Chapter A.6 Solutions
Calculus for Business Economics Life Sciences and Social Sciences Plus NEW
Ch. A.6 - Evaluate each of the following: (A)161/2 (B)16...Ch. A.6 - Convert to radical form. (A)u1/5 (B)(6x2y5)2/9...Ch. A.6 - Prob. 3MPCh. A.6 - Prob. 4MPCh. A.6 - Write the following expression in the form axp +...Ch. A.6 - Prob. 6MPCh. A.6 - Prob. 7MPCh. A.6 - Rationalize each numerator. (A)332 (B)2n4n...Ch. A.6 - Change each expression in Problems 16 to radical...Ch. A.6 - Change each expression in Problems 16 to radical...
Ch. A.6 - Change each expression in Problems 16 to radical...Ch. A.6 - Prob. 4ECh. A.6 - Prob. 5ECh. A.6 - Change each expression in Problems 16 to radical...Ch. A.6 - Prob. 7ECh. A.6 - Prob. 8ECh. A.6 - Prob. 9ECh. A.6 - Prob. 10ECh. A.6 - Prob. 11ECh. A.6 - Prob. 12ECh. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - Prob. 22ECh. A.6 - In Problems 1324, find rational number...Ch. A.6 - In Problems 1324, find rational number...Ch. A.6 - Prob. 25ECh. A.6 - Prob. 26ECh. A.6 - Prob. 27ECh. A.6 - Prob. 28ECh. A.6 - Prob. 29ECh. A.6 - Prob. 30ECh. A.6 - Prob. 31ECh. A.6 - Prob. 32ECh. A.6 - Prob. 33ECh. A.6 - Prob. 34ECh. A.6 - Simplify each expression in Problems 3540 using...Ch. A.6 - Simplify each expression in Problems 3540 using...Ch. A.6 - Simplify each expression in Problems 3540 using...Ch. A.6 - Prob. 38ECh. A.6 - Simplify each expression in Problems 3540 using...Ch. A.6 - Simplify each expression in Problems 3540 using...Ch. A.6 - In Problems 4148, multiply, and express answers...Ch. A.6 - Prob. 42ECh. A.6 - In Problems 4148, multiply, and express answers...Ch. A.6 - In Problems 4148, multiply, and express answers...Ch. A.6 - Prob. 45ECh. A.6 - In Problems 4148, multiply, and express answers...Ch. A.6 - Prob. 47ECh. A.6 - In Problems 4148, multiply, and express answers...Ch. A.6 - Write each expression in Problems 4954 in the form...Ch. A.6 - Write each expression in Problems 4954 in the form...Ch. A.6 - Prob. 51ECh. A.6 - Write each expression in Problems 4954 in the form...Ch. A.6 - Write each expression in Problems 4954 in the form...Ch. A.6 - Write each expression in Problems 4954 in the form...Ch. A.6 - Rationalize the denominators in Problems 5560. 55....Ch. A.6 - Rationalize the denominators in Problems 5560. 56....Ch. A.6 - Prob. 57ECh. A.6 - Prob. 58ECh. A.6 - Rationalize the denominators in Problems 5560....Ch. A.6 - Rationalize the denominators in Problems 5560....Ch. A.6 - Rationalize the denominators in Problems 6166....Ch. A.6 - Rationalize the denominators in Problems 6166....Ch. A.6 - Rationalize the denominators in Problems 6166....Ch. A.6 - Rationalize the denominators in Problems 6166....Ch. A.6 - Prob. 65ECh. A.6 - Prob. 66ECh. A.6 - Prob. 67ECh. A.6 - Problems 6770 illustrate common errors involving...Ch. A.6 - Problems 6770 illustrate common errors involving...Ch. A.6 - Problems 6770 illustrate common errors involving...Ch. A.6 - In Problems 7182, discuss the validity of each...Ch. A.6 - In Problems 7182, discuss the validity of each...Ch. A.6 - Prob. 73ECh. A.6 - Prob. 74ECh. A.6 - Prob. 75ECh. A.6 - In Problems 7182, discuss the validity of each...Ch. A.6 - Prob. 77ECh. A.6 - In Problems 7182, discuss the validity of each...Ch. A.6 - In Problems 7182, discuss the validity of each...Ch. A.6 - In Problems 7182, discuss the validity of each...Ch. A.6 - In Problems 7182, discuss the validity of each...Ch. A.6 - In Problems 7182, discuss the validity of each...Ch. A.6 - In Problems 8388, simplify by writing each...Ch. A.6 - Prob. 84ECh. A.6 - In Problems 8388, simplify by writing each...Ch. A.6 - Prob. 86ECh. A.6 - In Problems 8388, simplify by writing each...Ch. A.6 - In Problems 8388, simplify by writing each...Ch. A.6 - In Problems 8994, evaluate using a calculator....Ch. A.6 - In Problems 8994, evaluate using a calculator....Ch. A.6 - Prob. 91ECh. A.6 - In Problems 8994, evaluate using a calculator....Ch. A.6 - In Problems 8994, evaluate using a calculator....Ch. A.6 - In Problems 8994, evaluate using a calculator....Ch. A.6 - In Problems 95 and 96, evaluate each expression on...Ch. A.6 - In Problems 95 and 96, evaluate each expression on...
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