Answered: Let A and B be orthogonal n×n matrices.…

Let A and B be orthogonal n×n matrices. (i) Prove that A(AT + BT )B = A + B. (ii) Use part (i) to prove that if det(A) = − det(B), then A + B is not invertible.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Determinants

Section3.CM: Cumulative Review

Problem 29CM

See similar textbooks

Related questions

Q: [4x+5 if -1<x<2 3x-8 if 2≤x≤4 f(x) = { f(2)=

Q: find the equation of a line that passes through the point (5, -2) and is parallel to the line: x -…

Q: For simple interest, present value can be calculated using: OP=A-I OP=A+I OP= Prt OP=I-A

A: A = final amount (future amount)P= initial amount (present amount)I = interest amount

Q: Write an equation for the graph below in terms of 5 4 3 2 1 w & y = x-2 -1 744 N -3 54 -4 3 X

Q: A linear transformation T: R² → R2 is called a dilation if T(x) = rx for r> 1. (It is called a…

Q: Graph the quadratic relation Y = x 2 - 4

A: y=x2−4

Q: Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the…

Q: Which statement is true for a function y = -2(4x - 8)³ compared to the original, y = x³ Horizontal…

A: The given functions are:

Q: 3. Find the domain of these functions. (a) y = √3x + 4 x+5 (b) y = 5x-2

A: a) y= √(3x-4)b) y= (x+5)/(5x-2)We have to find domain of above functionsDomain: set of all value of…

Q: Find the average rate of change of the function f(x) = − 1x² + 6x + 4, from x=-1 to x=4. Note, the…

Q: K Use the graph of the function f given below to answer the questions. 60 Is there a local maximum…

A: Solution is given below.

Q: a) Function f(x) is defined as f(x) = i) Resolve f(x) into partial fractions. ii) Hence evaluate b)…

A: Since, you have posted multiple questions. As per guidelines, we are supposed to answer only first…

Q: A. C. 10 10 -5 -5 104 5 0 -5 10★ 5 0 -5 5 5 B. 10 10 D. 10 10 -5 y < 3x + 5 -5 104 5 0 -5 -int 104 5…

A: y<3x+5

Q: A clothing business finds there is a linear relationship between the number of shirts, n, it can…

A: Given that 1000 shirts are sold for $30 3000 shirts are sold for $10

Q: Let's say you have two similar polygons and the ratio of their perimeters is 4: 1. What is the ratio…

Q: One term in the expansion al * (x + a) ^ 7 = 756x ^ 5 Numeric Response The value of a, if a>0 is

Q: Given f(x) = x² + 7x + 25 and g(x) = -x² - 10x - 10, determine when f(x) ≤ g(x). 0-5 ≤x≤ -3.5 Ox≤-5…

Q: ca evoss 26 HAJON Six Dunces of an insecticide are mixed with 15 gal of water to make a Spray for…

A: Using unitary method, we can find the quantity of insecticide needed.

Q: a) The 3rd term of an arithmetic series is (5x + 5y) and the 6th term is (8x + 11y). Find, in terms…

Q: Find the solution of the exponential equation 100 (1.08)2 = 50,000 in terms of logarithms, or…

Q: Evaluate (-6 + 3i) + (-4 - 4i) - i² O-9-i O-11 +i O 10-i O-9-7i

A: We need to simplify the following expressionFormula Used:

Q: QB3% Let C=2+3i u= ( 1²/13 + 2/2 ²,0, 1/3-2²) v = ( 3²/3 + 4/1/², 1/3-2, 0) Calculate a) 2-3i b)…

Q: How many three-letter "words" can be made from 8 letters "FGHIJKLM" if repetition of letters (a) is…

Q: Find the equation of the parabola with the following properties. Express your answer in standard…

Q: K Given the function f described by f(c) = -5c+7, find the following. f(c + 2) f(c+2) = (Simplify…

Q: How long will it take $11,000 to grow to $16,500 at a simple annual interest rate of 5%?

A: Initial amount (P) = $11000Final amount (A) = $16500Interest rate (r) =5%=0.05

Q: What is the coefficient of x^6 in (2x + 3/x)^8?

A: To find the coefficient of in .Note: Since the student has posted multiple questions and does not…

Q: An ecologist is using birdsong recordings to study visits to a suburban garden. The software counts…

A: There are three types of birds Let number of magpie visits denotes by x Let number of rosella visits…

Q: Write a double integral that represents the surface area of z=f(x, y) that lies above the region R.…

A: f(x,y)=x2+y2R={(x,y):0≤f(x,y)≤36}

Q: 100 (19X - 30) = m

A: Given hereusing property of logarithmhere

Q: Let T: R² R² be defined by T Letu-de-{---G} = an and C= = V₁ = T(u) 3 - X1 X2 Ex: 5 , V2 = Find…

Q: Suppose that y is proportional to the cube of x, and that y = 5 when x = 7. What is y when x = 3?…

A: Mathematical form of the statement : y is proportional to the cube of xwhen,. .The value of constant…

Q: Solve: +5 = x+3 O-3 O 0-7 O-1 no solution x+4 x+1.

Q: If you were to use a substitution of u = cos(z) to evaluate the definite integral below, what would…

Q: Explain why “rationalizing the denominator” only changes the form and not the value of the original…

A: Note that when we rationalize through the denominator then it is done basically to make the…

Q: Molybdenum-99 is a radioactive element used in medicine (for example when performing a brain scan).…

A: Law of Decay where A is the amount after time t is the initial amount k is the constant t is the…

Q: Complete the table of values for y = x² - 4 -34 -2 -1 0 1 2 3 y

Q: U₁ = -0₁ --- --- -- = = V2 = (a) Find the transition matrix from the basis E = {v1, v2} to the basis…

Q: What type of relation is used to model compound interest? linear quadratic O exponential none of the…

A: Compound interest is the accumulation or addition of interest to a principal amount.

Q: Arrange the following fractions in ascending order without converting to decimals or finding…

A: We have to arrange the given fractions in ascending order.To solve problem like this first we take…

Q: The sum of three numbers is 15. The sum of twice the first number, 5 times the second number, and 6…

A: Given,the sum of three numbers is 15, sum of twice the first number, 5 times second number, 6 times…

Q: Graphing Transformations of a Quadratic Function The graph f(x) = ² is shown below. Let g(x) = f(x).…

A: The graph of is shown below.Let .To draw the graph of and to write its formula.

Q: A tinsmith wants to make a small windowsill planter from a 40 cm x 24 cm sheet of copper. She'll…

A: Given data

Q: Consider the following equation. Step 1 of 2: Find the x- and y-intercepts, if possible. 5y-2x = -10

Q: 4. Use the limit definition of the derivative to exactly evaluate f'(x). f(x) = ² H

A: Let a function f( x ) According to the definition of derivative

Q: FAVORITE MUSIC GENRE Jazz- 2% R&B Other 12% Classical 6% 2% Country -6% [4% Dance Rap hip-hop Rock…

A: Using the given circle graph, we can answer the question.

Q: 6 mi walking Walking at the Same rate, how many miles would a person need to walk to lose 116?…

Q: (a) How many days would it take you to spend $1 million if you spent $3 per minute? (Round your…

A: $1 million = $1,000,0001 m = 1,000 mm

Q: 2x³-3x-4 x² - 2x a) the horizontal asymptote(s) is/are = f(x) = Equation(s) required. Write none…

A: For vertical asymptote, equate denominor to zero and solve for x.For horizontal asymptote, solve the…

Q: 2 Let g(x)= -x + 3x + 4. Find g(p). g(p) =

Question

100%

Let A and B be orthogonal n×n matrices.

(i) Prove that A(AT + BT )B = A + B.

(ii) Use part (i) to prove that if det(A) = − det(B), then A + B is not invertible.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction:

Step 2: (i). Proof:

Step 3: (ii). Proof:

Solution

Step by step

Solved in 4 steps with 25 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Explain what it means in terms of an inverse for a matrix to have a 0 determinant.
Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.
11. Find two nonzero matrices and such that.
Can a matrix with zeros on the diagonal have an inverse? If so, find an example. If not, prove why not. For simplicity, assume a 22 matrix.
Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.