Let A = -48 -22] 110 51 Find two different diagonal matrices D and the corresponding matrix P such that A = PDP-¹. 0 -1921-1881 D₁ = 0 49:1-1881 D2₂ =

Q: Is the matrix A = 1|2 TILL -1 1 1 -1 -1 1 1 -1 1 1 -1 is orthogonal matrix.

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Q: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

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Q: Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

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Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: b) If P−¹AP and P-¹BP are both diagonal matrices, show that AB = BA.

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Q: Let 0 9. A = = [6 0 Is it possible to find a two by two real matrix B such that A = eB₂

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Q: 9. Show that the matrix 0 0 -1 0 0 1 -1 C2 = x, x- will transform the vector y into -y

A: We have to show that the matrix C2 will transform the vector in ℝ3 into the vector -x-yz. First we…

Q: 1 A = )Find the rank of a matrix 7 17 1 - 2 | 3.

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: Suppose A is a 2 × 4 matrix, and B is a 4 × 2 matrix. Assuming that A, B act on vectors in R",…

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Q: 1 31 A = 2 7 . A·B = B · A = I3×3 -2 -4 -5. ]

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Q: 30 14 Let A = -70 -33] Find a matrix P, a diagonal matrix D and P-1 such that A = PDP-¹. P = 3 D P-1…

A: This question from topic diagonalizable matrix from linear algebra.

Q: Find the LDU factorization of L = That is, write A = LDU where L is a lower triangular matrix with…

A: Given We need to find the LDU factorization of matrix A.

Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: 8. 3 a) Let A = ( 6 1 3 ,B = 6 -2/ %3D 1 Then find the matrix AB. -4 -1

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Q: <= [-5 1 is the product X = E₁ E₂E3 of elementary matrices E₁, E2, E3, find -5 35 E₁ = If x= 03-894…

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Q: 2. Consider the four matrices, 1 2 1 2 3 C = 4 5 6 1 2 3 4 3 A = 5 6 3 4 5 6 78 9 Solve for: а. АВ…

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Q: Find the general form of the span of the indicated matrices. (Use only x and w as variables in your…

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Q: 16 21 Let A = |-14 -19 Find two different diagonal matrices D and the corresponding matrix S such…

A: Given matrix is A=1621-14-19 We find the eigenvectors. For eigenvalues, A-λI=0⇒1621-14-19-λ…

Q: 1 -4-2) s) Let A := -2 3 2 4 -8-5 (a) Show that A is diagonalizable and find a nonsingular P such…

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Q: Use 8 ;] 0 y = -x, ON 9 -2 -5 -2 -5 2 -8 9-1 OB) 8-9 2 09112 -2 s -9 5 OD) -5 0¹/2²/ -25 12 DO 2 to…

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Q: If Q and U are unitary matrices, show that Q-1 is unitary and also QU is unitary. Start from QHQ = f…

A: As per the question we are given two unitary matrices Q, U and we have to show that Q-1 , QU are…

Q: 1 -1 2 a) Find the matrix A if (3A) =0 2 0 3 -1 4

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Q: -3 4 B = -1 | %3D 4 | 0 4 3. C = -2 5 1 D = 4 -2 0 1 Using the above matrices find DB

A: Given matrices are

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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Q: Select all of the following that are true for all nxn matrices A and B. AA²-A²A (A+BILA-B)-A²-B²…

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Q: Suppose A = *=([=3][=3][==] A6- -27 -15 50 28 = Find an invertible matrix P and a diagonal matrix D…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: Suppose that B = (CEED-·B·CD) -5 and C= 0 are ordered bases of R³. Find the conversion matrix from B…

A: Concept: A vector r is said to be a linear combination of vectors a ,b and c.. etc., if there exist…

Q: 2. (5pts) Find the LU factorization of the following matrix. 1 -3-5 -3 -1 -5 8 A= 4 2 -5-7 -2 -4 7 5

A: Step 1:Step 2:Step 3:Step 4:

Q: Factor these two matrices into A = XAX-¹: 4 = 3 A [

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Q: Use the matrix P to determine if the matrices A and A' are similar. -1 -1 P=[11] 2 p-1 = 6 [2] 15…

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