EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 13, Problem 9A
Raise the following numbers to the indicated power.
9.
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The set of all 3 x 3 upper triangular matrices
6) Determine whether each of the following sets, together with the standard
operations, is a vector space. If it is, then simply write 'Vector space'. You do not
have to prove all ten vector space axioms. If it is not, then identify one of the ten
vector space axioms with its number in the attached sheet that fails and also show
that how it fails.
a) The set of all polynomials of degree four or less.
b) The set of all 2 x 2 singular matrices.
c) The set {(x, y) : x ≥ 0, y is a real number}.
d) C[0,1], the set of all continuous functions defined on the interval [0,1].
7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and
show that it is orthogonal to both u and v.
8) a) Find the equation of the least squares regression line for the data points
below.
(-2,0), (0,2), (2,2)
b) Graph the points and the line that you found from a) on the same Cartesian
coordinate plane.
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1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix
A.
= [{² 1]
A =
b) Verify that PT AP gives the correct diagonal form.
2
01
-2
3
2) Given the following matrices A =
-1
0
1] an
and B =
0
1
-3
2
find the following matrices:
a) (AB) b) (BA)T
3) Find the inverse of the following matrix A using Gauss-Jordan elimination or
adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I).
[1 1 1
A = 3 5 4
L3 6 5
4) Solve the following system of linear equations using any one of Cramer's Rule,
Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and
check the correctness of your answer.
4x-y-z=1
2x + 2y + 3z = 10
5x-2y-2z = -1
5) a) Describe the zero vector and the additive inverse of a vector in the vector
space, M3,3.
b) Determine if the following set S is a subspace of M3,3 with the standard
operations. Show all appropriate supporting work.
Please help solve the following whilst showing all working out. Is part of exam revision questions but no solution is given
Chapter 13 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 13 - Subtract 7516278 .Ch. 13 - Multiply 7238 . Express the result as a mixed...Ch. 13 - Multiply 1.7022.35 .Ch. 13 - Prob. 4ACh. 13 - Prob. 5ACh. 13 - Prob. 6ACh. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...
Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the diameters and heights...Ch. 13 - In the following table, the diameters and heights...Ch. 13 - In the following table, the diameters and heights...Ch. 13 - In the following table, the diameters and heights...Ch. 13 - Prob. 55ACh. 13 - Prob. 56ACh. 13 - Prob. 57ACh. 13 - Find the area of this plate. All dimensions are in...Ch. 13 - Find the metal volume of this bushing. All...Ch. 13 - Find the volume of this pin. All dimensions are in...Ch. 13 - Prob. 61A
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- please help me with this question with working out thanksarrow_forwardPage < 1 of 2 - ZOOM + 1) a) Find a matrix P such that PT AP orthogonally diagonalizes the following matrix A. = [{² 1] A = b) Verify that PT AP gives the correct diagonal form. 2 01 -2 3 2) Given the following matrices A = -1 0 1] an and B = 0 1 -3 2 find the following matrices: a) (AB) b) (BA)T 3) Find the inverse of the following matrix A using Gauss-Jordan elimination or adjoint of the matrix and check the correctness of your answer (Hint: AA¯¹ = I). [1 1 1 A = 3 5 4 L3 6 5 4) Solve the following system of linear equations using any one of Cramer's Rule, Gaussian Elimination, Gauss-Jordan Elimination or Inverse Matrix methods and check the correctness of your answer. 4x-y-z=1 2x + 2y + 3z = 10 5x-2y-2z = -1 5) a) Describe the zero vector and the additive inverse of a vector in the vector space, M3,3. b) Determine if the following set S is a subspace of M3,3 with the standard operations. Show all appropriate supporting work.arrow_forwardUsing Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates).arrow_forward
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- Find the sum of products expansion of the function F (x, y, z) = ̄x · y + x · z in two ways: (i) using a table; and (ii) using Boolean identitiesarrow_forwardThe NOR operator, denoted as ↓, behaves as 0 ↓ 0 = 1, 0 ↓ 1 = 0, 1 ↓ 0 = 0,1 ↓ 1 = 0. Show that the any Boolean function over any number of variables can be expressed using onlyNOR operators (in addition to those variables and constants). HINT: Recall that any Boolean function hasa representation as a sum of products expansionarrow_forwardConsider the Turing machine given in lecture which decides the languageB = {w#w | w is a binary string}.Simulate the Turing machine to show that the string 1001#1001 will be accepted by the Turing machine. Show all steps.arrow_forward
- Q/Find the Laurent series of (2-3) cos↓ around z = 1. 2-1arrow_forward#1). A technique is given with 150 mAs is 40 kV and produces an EI value = 400. Find the new EI value, if mAs is 75 and 34 kV are used.arrow_forwardQ3: Answer the following: (i) Let f(z) is an analytic function in a simply connected domain S and y is a simple, closed, positively oriented contour lying in S. Prove that f, f(z)dz = 0.arrow_forward
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