() Q = x2 + y? + + 2xy = (x y z)A | y where A is a hermitian matrix. Then the three column vectors for a unitary matrix U such that U-'AU is diagonal are: () () --() 00-0 V3 and v2 1 and 1 and V3 and v2 None of the given options is correct

Q: Find the 2 x 2 matrix P such that Po is the orthogonal projection of in R2 onto the line consisting…

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Q: B) Suppose A is an invertible matrix inM, (R). And x, y E R". Prove it: det(A+ ry") = (1+y"…

A: Given: A is an invertible matrix in Mn(ℝ) x,y∈ℝn To prove: det(A+xyT)=(I+yTA-1x)det(A)

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A: We have to Find T(v) by using the standard matrix and the matrix relative to B and B.   Given…

Q: Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) = x" Ax sa} + 3.x3 +…

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Q: 21.1f A' = 34² where A is n by n matrix, then (a) A= 31 (b) A 31 if rank((A) =n () A" =!1 (d) a and…

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Q: ) If the matrix A= [4 2 1; 1 5 9; 3 8 7], find: · A' - A(3,1) - size(A) - A(:,2)= [] Inv(A)

A: Since, you have posted a question with multiple sub-parts, as per company policy we will solve first…

Q: Find the coordinate matrix of w = (5, −5, 2) relative to the orthonormal basis B for R3 below.

A: Basis: A set of vectors S is said to be a basis of the vector space V if the set S is linearly…

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

Q: ( ). For matrix A = if f(X) = (X+ 2)(X – 2), calculate f(A)? -16 33 17 (17 48' В. 16 33. A. -48 -48)…

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Q: snip

A: The determinant of an orthogonal matrix is always one. Therefore to prove that the given matrix,…

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A: we have, matrices A, B and C of appropriate sizes, By definition of invertibility of matrices , we…

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Q: 3. Let vi - [1,-2,3], va -(-1,-4,5], and va [5,-1,3] be vectors in R'. a) Use determinant to show…

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Q: Show that if annxn matrix U satisfies (Ux)· (Uy) = x•y for all x and y in Rn, then U is an…

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Q: 1) Determine whether the given vectors are linearly dependent or linearly independent. a)…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: TV T(x, y,2)=(xry, q-2, x-2) 1. Fond the matrix A represmting T Fnd matrix B repregenty 2. 3.…

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Q: 2 -2/2 2/2 , show that A and B satisfy 2 Q#5: If A= and B 2 commutative property with respect matrix…

A: Given  A=2-2222  and  B=222-22. We have to show that  AB=BA.

Q: 0 1 1 (₁2) (₁) (1₂) Calculate matrix = = (A – AT)² and vector w = Bx. Then, Consider matrix A = X =…

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Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". 3 10 -), (o, 1, 0), 0, 10…

A: To solve the following problem and find the coordinate matrix of x

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Q: Let J„ be the n × n matrix whose entries are all equal to 1, and let D(^1, ... , An) be the n × n…

A: The complete solutions are given below

Q: Prove det(A) = det(A'), for an upper triangular matrix A.

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Q: and ß that solve the vector equation: a (²) + ( )= (²²) (21) B 3 28

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Q: Let A, B, C and D be invertible n xn matrices with n> 7, which satisfy the equation ABCT DBA"C = ABT…

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Q: Let T: R³ → R² be defined by T -~--~--E) ----B]}~~(~-| ||-~ ~[]) Let B = u₁ U3 = { = [3], , = 6 (ED)…

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Q: V has bases B = (v1, v2, v3) and B' = (w1,w2, W3). If wi vị + 2v2 + 4v3, wz = 2v1 + 5v2 + 6v3, wz =…

A: Given that, B=(v1,v2,v3),B'=(w1,w2,w3) Given that,…

Q: If the matrix A= [2 5 1;7 3 6;2 5 4], find: A' A(2,3) size(A) LA(:,2)=[] Inv(A)

A: We can solve this as follows:

Q: 2. Find the matrix of the linear operator L: P₂ (R)→ P₂ (R) defined by L(c+bx+ar²) = c+(a+b)x² with…

A: To determine the matrix for a linear transformation. Find the value of linear transformation on…

Q: 7. Show that the matrix A=I– 2vv' , where v is a unit vector in R", and I is an nxn identity matrix,…

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