Q2: Let A, B be matrices of size 3x3 such that and AB = A+2I A = -101 21 2 find A, B?

Q: A? 0 0 A =

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Q: Let A and B be 2x2 matrices such that B is invertible If detA)2 and det)-, then detA'e) Select one:…

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Q: 1. By hand, find the QR factorization of the matrix

A: QR factorization means A = QR Where, Q is an orthogonal matrix with orthogonal columns and R is an…

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 2 -4 A = 4-4 3. - 1 18 -3

A: The LU factorization of a matrix A is writing A as the product of matrices L and U, where L is a…

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-'AP is diagonal. (If not…

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Q: Solve for the matrix X if AX(D+BX)~' = C. Assume that all matrices are n X n and invertible as…

A: Given that AXD+BX-1=C Pre-multiply by A-1 A-1AXD+BX-1=A-1CXD+BX-1=A-1C post multiply by D+BX…

Q: Q1: Let A= B 3 1.Find the values of a and B for which A is 01 3 1. Non-singular. 2. SDD. 3. PD. For…

A: 1. A=α20β31013A is non singular⇒A≠0A=α9-1-23β-0+0β-0       =8α-6β

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 – 2xy – 2xz –…

A: Step:-1 Given quadratic form is  Q=2x2 +2y2 +2z2 -2xy -2xz -2yz Q=xyz 2-1-1-12-1-1-12 xyzQ=XTAXHere,…

Q: Find the matrixx such that 2A + B + X =0 where 1 2 3 -2 A = %3D 3 4 1 5 Select one: a. -1 -2 -7 13

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Q: Find x such that the matrix is singular. 4-[94] A

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Q: |adjA| = |A]"=1 n-1

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Q: Find 2 X 2 matrices A 0 and B # 0 such that AB = 0. Can you find a matrix A + 0 such that A2 = 0?

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Q: Let A and B be square matrices of order n satisfying Ax = Bx for all x in Rn. (a) Find the rank and…

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Q: - |A°| |B°| • |4°|

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Q: Let A and B be n × n matrices and let x ∈ Rn. How many scalar additions and multiplications are…

A: Let A and B be n × n matrices and let x ∈ Rn

Q: Q9. As usual, let In denote the n x n identity matrix. 1 - (a) Find a 2 × 2 matrix such that A² =…

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Q: Let A and B be 3 x 3 matrices such that A 3 = B 6 l10! The matrix C = A – 2B is invertible. %3D [5.

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Q: Let A, D, and P be n × n matrices satisfying AP = PD. Assume that P is nonsingular and solve this…

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Q: Which of the following matrices is a nilpotent matrix of degree 2. a a) where ab =-x². -x a where ab…

A: We have to select the nilpotent matrices of order 2 from the above list.

Q: Solve for the matrix X if AX(D + BX)-1 = C. Assume that all matrices are n X n and invertible as…

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Q: Let A and B be square matrices of order 2 such that |B| = 4 .What is ( AB) '

A: To see 2nd step

Q: Find a 2 x 2 matrix B so that B2 = A, where

A: Given matrix A=-7-16817 To find matrix B such that B2=A.

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: Let A and B be symmetric n × n matrices and let C = AB. Is C symmetric? Explain.

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Q: Find all a,ß>0 so that the matrix 3 2 B [4]= a 5 B 2 1 a is strictly diagonally dominant.

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 3 -21…

A: Given;                           A=13-223001-1 Start with A I…

Q: Q3: Express A and A-1 as a product of elementary matrices. [1 0 5] A = 0 1 6 li o 3]

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Q: Find two 2 × 2 matrices A such that A2 = I.

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Q: Q4: If the matrix A = (; :),s Show that A2- 2A – 21 = 0.

A: We observe that characteristics eqn of A will be x^2-2x-2=0. By Caley hamilton tum put x=A we get,…

Q: Solve for the matrix X if AX(D+BX)-! = C. Assume that all matrices are n x n and invertible as…

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Q: ?) A is an n x n matrix, such that 2A3 – 4A? + 6A – 21 = 0 (where I is the identity matrix and 0 is…

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Q: Solve for the matrix X if AX(D + BX)-! = C. Assume that all matrices are n X n and invertible as…

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Q: Find the symmetric matrix that corresponds to the quadratic form q(x, y, z) = 3x² + 4æy – y² + 8xz

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Q: Let A be a 3 x 3 matrix such that 3a(1)- 2a(2)+7a(3)=0. Is A nonsingular? Explain.

A: A is singular matrix if rank is not full

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: Q5. Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is…

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Q: For the matrix A, find an orthogonal matrix P such that P-'APis diagonal. 3 00 A =| 0 2 2 0 2 5

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Q: Let A be an n x n matrix and let D be a n x n diagonal matrix. Show that AD =…

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Q: Let A and B be n × n matrices and let x ∈ Rn. How many scalar additions and multiplications are…

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Q: .

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Q: b) Consider the matrices C and D: C = D = -8 2 at 8.49.35 AM Calculate matrix 2C + 3D.

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Q: Find the value of k such that matrix A is 2. k – 10 singular on Ik - 5 а. 1 С. 3 b. 2 d. 4 O D O B O…

A: Topic = matrices Correct option=D

Q: If a and b are the matrices of order 3 and (A)=5,(b)=3 then find the vailue of 3ab?

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Q: Find two different 2 x 2 matrices A such that 1 0 A? =

A: Given: A2=1001

Q: Let A and B be square matrices of order 2 such thatA=-7 and B=4.What is (ABY"| %3D %3D

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Q: Let A, B, C be n × n matrices and assume that A is invertible. Solve the equation A(B + X) = C for…

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Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3.…

A: Given :          A = 13-223001-1   To find the inverse of A. Also, to compute 3A-1.

Q: a Let A = b be 2 x 2 matrix such that d 3A' +2 Find A. 1

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