a. To find: A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B .

Question

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Answer 1

Question

Chapter 14.CR, Problem 13CR

To determine

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

To determine

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

To determine

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

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Page < 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.

13) Let U = {j, k, l, m, n, o, p} be the universal set. Let V = {m, o,p), W = {l,o, k}, and X = {j,k). List the elements of the following sets and the cardinal number of each set. a) W° and n(W) b) (VUW) and n((V U W)') c) VUWUX and n(V U W UX) d) vnWnX and n(V WnX)

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Answer 2

Question

Chapter 14.CR, Problem 13CR

To determine

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

To determine

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

To determine

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

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Answer 3

Question

Chapter 14.CR, Problem 13CR

To determine

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

To determine

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

To determine

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

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Answer 4

Question

Chapter 14.CR, Problem 13CR

To determine

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

To determine

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

To determine

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

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Answer 5

Chapter 14.CR, Problem 13CR

To determine

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

To determine

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

To determine

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

Answer 6

Chapter 14.CR, Problem 13CR

To determine

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

Answer 7

Chapter 14.CR, Problem 13CR

To determine

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

Answer 8

To determine

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

Answer 9

To determine

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

Answer 10

To determine

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

Answer 11

To determine

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 14.1 - Prob. 1MC Ch. 14.1 - Prob. 3MC Ch. 14.1 - Prob. 5MC Ch. 14.1 - Prob. 6MC Ch. 14.1 - Prob. 7MC Ch. 14.1 - A drawing of a cube, shown in the following...Ch. 14.1 - Wall stenciling has been used to obtain an effect...Ch. 14.1 - Prob. 10MC Ch. 14.1 - The following figure is a partial tessellation of...Ch. 14.1 - Prob. 12MC

a. To find: A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B .

Solution Summary: The author explains how to find a single transformation from A to B, followed by two translations from B to C.

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

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Chapter 14 Solutions

a. To find: A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B .

Solution Summary: The author explains how to find a single transformation from A to B, followed by two translations from B to C.

a. To find: A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

b. To find: The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

c. To find: A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.

Want to see the full answer?

Chapter 14 Solutions

a.

To find:

A single transformation for (i) a translation from A to B followed by a translation from B to C and (ii) a translation from B to C followed by a translation from A to B.

b.

To find:

The single rotation about point O by 90° counterclockwise, followed by a rotation about O by 30° clockwise.

c.

To find:

A single dilation for (i) a dilation with center O and scale factor 3 followed by a dilation with center O and scale factor 2 and (ii) The dilations in part (i) in reverse order.