3) Consider the following matrix: [2 sin² a 2 cos² a 1] A = 2 sin? ß 2cos² ß 1 [2 sin² y 2cos²y 1] Answer the following questions: 3.1) Without using cofactor expansions, find det(A). 3.2) What can we say about the reduced row-echelon form of A?

Q: 2.3 Compute the principal square root of each of the llowing positive semidefinite matrices. (b) 2 3…

A: Please find the solution in next step

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A: To find- Determine the gradient and the Hessian of the following function fx = αx2 + Ax - b2 where x…

Q: Let A 1B = 5 l, and C-1 = If X is a matrix that satisfies: %3D %3D 2B = Al2 - XC then X is

A:

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: 1 : Find the inverse of the matrix 1 -1 0 A = 3 -1 2 with using the method of Cofactor (Adjoint).

A:

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A: Since, matrix P is invertible. This implies P-1 exist. Let A and P be matrix such as Find the…

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Q: Due to what property, applied to the matrices and scalars below, do we know that (cd)A = c(dA)?

A:

Q: You are given the set M(2Z) of 2 x 2 matrices with even integer entries. The notation 2Z denotes the…

A:

Q: Examine the nature of the following matrix defined by A = [0        1 + 2i       −1 + 2i      0  ]…

A: Given:  A=01+2i−1+2i0 To explain nature of above matrix and to find its proper values and proper…

Q: a) Factor the matrix A into the product XDX- where D is diagonal. (-1 -2 2 A = 4 3 -4 -2 b) Verify…

A:

Q: 12. Find two different 3 x 3 matrices A and B such that the associated quadratic forms equal q(7) =…

A:

Q: Which of the following is not a step involve in Gauss Jordan Method? (A) evaluation of cofactors B)…

A:

Q: Use the results of LU decomposition 1 -3 -1 A=LU=|3/2 li/2 1 0||0 1/2 -1/2 1] Lo 1 1 to solve Ax=b,…

A: To solve the equation Ax=b using LU decomposition, given that A=LU=100321012112-3-1012-12001 and…

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Q: 1. Solve the initial value problem by using the fundamental matrix (using other methods are not…

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Q: (i) Use the properties of trace to argue that tr(AʼA) = tr(AA') for any n × m matrix A. [2 0 (ii)…

A:

Q: 4. Consider the 3 x 2 matrix A such that A - and A (a) Write down A. (b) Is A singular? Justify your…

A: 4. The given equations are,A.12=201 and A.21=201

Q: Show that if a square matrix A satisfies A2 − 4A + I = 0, then A is invertible and A−1 = 4I − A.…

A:

Q: 4. Suppose that the matrix P has the following eigenpairs: d1 = 4, v1 = A2 = -5, v2 = Write the…

A: The general solution of given system is given as follows :

Q: Refer to Matrix A and B, determine the following 6. co-factor of az21 and a33 of A? 7. determinant…

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Q: 2 x + y + z = 2 −3x+3y−3z= 9 −x +7y +3z = −11 Compose the augmented matrix corresponding to this…

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Q: -1 [A] = 4 3 -3 2 %3D L3 1] 2.

A: Given :                    2-134-32321 To find :                 The cofactors for C13 , C22 , C32…

Q: Compute the determinant of 15 2 4 3 4 1 A = 0 03 4 0 7 4 7 (a) by using a cofactor expansion across…

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Q: Consider the following nonhomogeneous linear system: xi = 3x1 + 4x2 + 10 cos t x2 = 3x1 + 2x2 %3D 2.…

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A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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Q: Is the following matrix a Hermitian or Skew-He rmitian, and find the 2 3 – 2i 1+i A X = -3 – 2i 2…

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Q: If the extended st ress at the point p in the level and at i+ j+ k is given by matrix 10 2 222 the…

A: Solution: Matrix is 102222231 and n^=13i+13j+13k

Q: Suppose that column 3 of a 3 x 6 matrix is all zeros Then is a special solution Ob. is a specolution…

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Q: 1 Find the real constants a and b in the matrix Q - a such that Q is orthogonal b

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Q: d the third column of A 'without computi 1 be found without computing the other om nted matrix (A…

A: The matrix is given as A=-2-3-2525431218. To determine the third column of A-1 without computing the…

Q: а? а.b а. с a? ab cos y ac cos B = b. a b? b.c = ab cos y bc cos a С.а с.b с? ас cos B bc cosa =…

A: Consider the given matrix :A=a2a.ba.cb.ab2b.cc.ac.bc2   =a2ab cosγac cosβabcosγb2bc cosαac cosβbc…

Q: 10 choose a,b,c,d

A: 1. Option a is wrong as the columns of D are LI hence solution will be unique if exists. 2. Option b…

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Q: find A-1 using Gaussian elimination and check the resul 3 -2 [1 1) A = |1 2 4. 27 1 1 Ans: A-1 = -2…

A: Explanation of the answer is as follows

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Q: 5. Show that if M is a 3 x 3 magic square with weight w, then we can write M as M = Mo+ kJ where Mo…

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Q: 2. Find a single matrix equal to [1 - i 1+0, where i = √-1 (imaginary unit).

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Q: Find the singular values of the given matrix.

A: Consider the given matrix, A=2102

Q: Use the results of LU decomposition 1 2 -3 -1 A=LU=|3/2 l1/2 1 0 1/2 -1/2| 1 1] Lo 1 to solve Ax=b,…

A: Consider the matrix: A=100321012112-3-1012-12001……1bT=1-11……2   Also, AX=b……3

Q: Using Laplace expansion, the 4x4 matrix will be reduced to 4 terms with a 3x3 minor determinant.…

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Q: Consider a 3 × 3-matrix whose first row is a vector a, the second row is a vector b, and the third…

A: given row  of  3×3  matrix  is          a   , vector      b   , vector c=2a+3b    , vector