a +b b-a a,b eR Given the following matrix: A=la-b b+a) Under what conditions on a , b The matrix A is orthogonal?

Q: What conditions must a and b satisfy for the matrix to be orthogonal? [a +b b- a] la - b b+al

A:

Q: (a)If A-[ ay] is a 3x3 matrix; such that ay =i(4-), find the values of %3D diagonal elements and the…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: If Q = I - auu" where Qis an orthogonal matrix, a > 0, and u E R"X1 real vector, and I is n x n…

A:

Q: lb Given a 3 × 3 matrix in terms of a scalar e and that det(A) = 8 , find the value(s) of c if -1 3…

A: Since you have asked multiple question, we will solve any one question for you. If you want any…

Q: If A,B,C are nxn invertible matrices and I is nxn unit matrix C-(A + X)B¬1 = I What is the solution…

A: Given that C-1(A+X)B-1=I   To Find: X=?…

Q: Given vectors u = (5,0,0), v = (-2,-1,0), and w = (3,7,2), %3D %3D a) Determine if the vectors u, v,…

A: a) u=5,0,0,v=-2,-1,0,w=3,7,2     write it as…

Q: Give the 4 x4 matrix that rotates the points in R° about the z-axis through an angle of - 60°, and…

A: Given:     Angel = -60°      p = ( 4 , -2 , 6 )

Q: Question B. 2 1 0. 2 0 1 B1 : 0 2 0 and B2 0 2 0 %3D 0 0 2 0 0 2

A: We have to check whether the matrices B1=210020002 and B2=201020002 are similar or not. For this, we…

Q: Let A, be Hermitian matrix witho (A) = 1,-1 and B, is a Hermitian matrix with o (B) = 0,-2, then one…

A: We have to solve given problem:

Q: The rank (i.e., the number of pivots) of the matrix 4 1 2 1 2 1 1 0 0 1 2 -1 0 0 2 1 1 1 2 2 8 1 2.

A:

Q: 1. Let A be the matrix given by 1 A = 1 2 1 0 1 3 Find Cartesian equations for Col(A) and Null(A).…

A:

Q: Consider the matrix X and the vectors y and z below: x-E ] -- --| X= y= a. What is the inner product…

A: Answer

Q: This is a linear algebra problem. Please explain each step thoroughly. Give an example of a 2 x 2…

A: Let us consider an example. Let A=1112 And U=10, V=01 Then U⋅V=1⋅0+0⋅1=0 Hence, U and V are…

Q: Let A be a matrix with linearly independent columns. Select the best statement. A. There is no easy…

A:

Q: 2 and C = B are bases for R?. Complete the augmented matrix used to find the change of coordinates…

A:

Q: A=18, B=22 Give a 2x2 matrix that will project any point (x, y) on to the line going through (0, 0)…

A:

Q: - E- is multiplied by is equal to zero, then matrix If matrix A 3 B1 C.o D-2

A:

Q: [1 0 2] 1 2 is diagonalizable. Justify your answer. 0 0 0 9. Determine if the matrix A = 1

A: If minimal polynomial having a repeated roots then that matrix is not diagonalzible.

Q: Consider the matrix [3 0 -2] A =1 2 1 -5 2 -1 a] Use the Gaussian elimination with pivoting and…

A: Given matrix is. A=30-2121-52-1 Given system is Ax=b where b=2-31. So the system becomes.…

Q: Let A be a 3 x 3 matrix with columns a1, a2, a3. Suppose that A has the following properties: • aj…

A: Columns a1 and a2 are linearly independent and the third column can be written in terms of a1 and…

Q: (1) 2 (c) Let A = -1 0 Find an orthogonal matrix P such that PT AP = D where D is a diagonal matrix…

A:

Q: 17 The vector -14 is a linear combination of the vectors -5 and 7 if and only if the matrix equation…

A:

Q: 5 7 2) 3 1and B -1-2 0 10 ( 5. The Matrix A and B are a non nxn matrix. Given that A= 2 11( %3D -5…

A: Given that A=572231-1-20 and B-1=100110-5-21 (a) The objective is to find A-1. Determinant of matrix…

Q: a) ir(A - 1)1- ( -2) %3D Find the matrix A

A:

Q: condition must a and b satisfy for the matrix to be orthogonal? a – b b+a

A: We find the condition on a and b

Q: If Q = I- auu' where Qis an orthogonal matrix, a > 0, and u e R"x1 real vector, and I is n x n…

A:

Q: 2- For asymmetric matrix 3x3 matrix dij =0 if, a) i+j=0; b) i-j=0; c) i-j=1. 3-For a symmetric nxn…

A: Symmetric Matrix

Q: [1 2 1] A = 2 0 2 l2 3 kl give matrix. [A| = 1 , k=?

A:

Q: Let 2 -1 A = 1 -1 0 2 Find an orthogonal matrix P and a diagonal matrix D such thatt D = P"AP. D =…

A:

Q: Consider matrices A E F"," , b E F",. Select all true statements about system of linear equations Ax…

A: Let A∈Fn,n,b∈Fn,1 and the system of linear equation is Ax=b The given statements are: 1. If the…

Q: E A be the matrix given by 3 1 0 1 2 1 A = 3 1 0 トつ (based on the definition of linear…

A:

Q: Q. No. 2): 1 4 Let 0 3 1 be the augmented matrix. Denote the columns of A by v, and y, .and -2 6 h-8…

A: 1. Consider A=1003-26, B=41h-8 and given h=58 Now A:B=1003-2641h-8=1003-264158-8=1003-264150 Rank of…

Q: [ -2 2 Let A = 2 i Find a matrix P that orthogonally diagonalizes A. Then, verify that 1 the…

A: Given that,A=-2221The matrix P that orthogonally diagonalizes A is determined as shown below.

Q: The rank (i.e., the number of pivots) of the matrix 4 1 2 2 1 1 1 1 1 0 1 2 -1 0 0 2 ] 1 2 2 8 1 2

A: We have to find the rank of the matrix.…

Q: Consider the system of equations. Edit 1 1 3. 3 3. 1 1 1 X. 1 Find a fundamental matrix for the…

A: The fundamental matrix is phi(t)=psi(t)×psi-1(0)

Q: -3 i. If A =0 then show that A3 – 9A + 101, = 4, where I, and o -3. 3 -1 are unit matrix and null…

A: Given a matrix A=2-320203-1-3 To show that A3-9A+10I3=φ, where, φ is a null matrix and I3=100010001.…

Q: A. What conditions must a and b satisfy for the matrix to be orthogonal? [a + b b-a] la -b b+al

A:

Q: Matrix AA is transformed by a scalar to form matrix BB . A=[−1.5   3]       B=[3   −6] [4.25…

A:

Q: Q. No. 2): 1 0 4 Let 0 3 -2 6 h-8 1 be the augmented matrix. Denote the columns of A by v, and v,…

A: Given: Augmented matrix 104031-26h-8, h-8 = -6, A = 1203-26 and b = 41h-8

Q: 1 [1 v2 LO (a)Non Orthogonal 1 5- The matrix A = is (b) Unitary (c) Diagonal (d) Orthogonal

A: Given that A=12110-1 To check if A is Non-Orthogonal Unitary Diagonal Orthogonal

Q: i) Find B Use Desmos Matrix 3 A = B = [ -6 6 4. -7 -8 II

A:

Q: and C are bases for R². B= 9. -8 Complete the augmented matrix used to find the change of…

A:

Q: [1 b+1] The value of b such that the det(A) = -1 is 8. Given the matrix A %3D 3. . Thus the matrix A…

A: The given matrix is A=1b+138 and detA=-1To find the value of b.

Q: ® Given 1 is a solution for the matrix equation A8=B. Determine and explan why each statement is…

A:

Q: 4. Determine whether the given matrix is orthogonal. Give detailed explanation 1 1 1 3 2 5 1 A : 3 1…

A: The answer is found in step-2

Q: MATRIX A Is axa T ElbENUALUES ARG -3 AルD a FWD CHE EI6EN. VALUES Fere A+3I IS

A: As we know that; If the λ1 & λ2 is eigenvalues of the matrix A then eigenvalues of the matrix;…

Q: The set of non-zero vectors {b, b2, b,, b4} are vectors in R* with the property that 4b, + 2b, = 6b,…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: a hh X1 Let A = gCa be a matrix with |A = 2 Then for the vector of unknowns X = and X3 the vector of…

A: The given system of equations has three equations and three unknowns. Also, as the determinant of…

Q: (c) State the definition of an orthogonal matrix. Explain mathematically the two sentences: (i) A is…

A: