Complete the matrix A so that it is Hermitian. 6 – 3i 1 A = -4 1 2 2 =

Q: Let a Consicler the matrix 121 4) S23. A=/S. 87.3 Find Miz, Ci2 and M2z Czt

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Q: Use software of your choice to compute T2, T, T®,T16 – this is most easily accomplished by squaring…

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Q: (a) Approximate the value of fcos (0.64 sin x) dx, using two and three points Gauss Quadrature where…

A: Note:  Hi! Thank you for your question. As there are two questions so as per our guideline we are…

Q: 2+i 3 -1+3i If A = -5 i 4-2i show that AA is a Hermitian matrix, where A is the conjugate transpose…

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Q: Find a matrix B such that AB = I, where 6 1 A = 1 0 0 1 and I = -6 6 a b Hint: Let B =c d

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Q: ind the adjoint matrix of A and then find the nverse 1 2. A = 2 3 1 4, 2) 2.

A: Solution: The objective is to find adjoint and inverse of the given matrix

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: sin 20=sec (1i) Show that the matrix M is invertible, where 3 -2 5 M=7 4 -8 %3D 5 -3 -4 Hence, find…

A: To show that the matrix M is invertible and to find the inverse of M

Q: Determine whether th e given matrix is orthogonal. If it is, find its inverse

A: Given: To Find: (a). Whether the matrix is orthogonal. (b). If orthogonal find it's inverse.…

Q: Let a Consicler the matrix 4. A= S23 87.3. Find Mz, C1z and Mzz, Czz

A: Given,A=214523873If A=a11a12a13a21a22a23a31a32a33ThenM12=a21a23a31a33 And C12=(-1)1+2M12 And…

Q: Need help finding the Jordan Canonical Form, an invertible matrix P such that J=P^-1MP And J^9

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

A: Let A be 4×4 matrix that rotates the points in ℝ3 about the z-axis through an angle of -60° is,…

Q: Which of the matrices that follow are Hermitian? Normal?

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Q: o 1 0] If A=|0 0 1 then show that, A = pI +qA+rA² where I is the identity matrix of order 3. p q r

A: For a square matrix A of order n  |A−λI|=(−1)n[λn+a1λn−1+a2λn−2+...+an]  and the characteristic…

Q: +i) is unitary and find A. Prove that the matrix A =

A: Given: A = 121+i12-1+i121+i121-i To do: Prove that A is unitary. Find A-1.

Q: Identify the Hermitian matrix 9i 1+ 2i -2i 2 -7i (a) 3i 1+ i (b) 7i [2i 1-i -9i 1- 2i 3 1 i -2i] 1…

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Q: Determine the cofactor of 2 in the matrix A = 1 9. 7 4 O-4 3. O -3 2.

A: Cofactor of any element aij is the determinant of the matrix formed by deleting row i and column j…

Q: [O 1 0 If A =0 0 1 then show that, A = pl + qA + rA where I is the identity matrix of order 3. %3D…

A: The given matrix is A=010001pqr To prove A3=pI+qA+rA2

Q: Give the 4x4 matrix that rotates the points in R about the z-axis through an angle of -30°, and then…

A: We have to find the 4×4 matrix that rotates the points in R3 about the z-axis through an angle of…

Q: 0 Find a non-zero 2 × 2 matrix A such that A? 0 0 A =

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Q: tet A be an x n matrix satisfying A-3A + 1, = 0 where O is the nXnzero matrix. Then A-1 = 31, – A²

A: i have provided solution in step2.

Q: Find the coordinate matrix of x relative to the orthonorm x = (10, 20, 5), B = {(÷, 0). (- ÷ [x]B =…

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Q: Identify the Hermitian matrix 9i 1+ 2i 1 -2i 2 -7i (а) 3i 1 +i (b) 7i 2 l2i i -9i 1- 2i 1 i -2i] 1 2…

A: Hermitian matrix is equal to its own conjugate transpose.

Q: Q: Find I 3 (adj cA)"+ A) where A matrix of size 4x4 such that IAI=3 is a that sotis

A: By using some basic properties of matrix we can solve it

Q: The matrix A = has a singular value decomposition A = UEVT where U = and [5/2 3/2 and V = The 2,2…

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Q: 1+ai Let a, b, c E R. Given that the matrix 4+2i 2144 1+ ci is Hermitian, the values of a, b and C…

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Q: I find the cooridinate matrix for A realtive to S=SA, Ag „Az, Au? where A= [2 0 and 1 1 00

A: The coordinates matrix for A is [a b c d]=aA1+bA2+cA3+dA4=A .see 2nd step.

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: Which of the matrices that follow are Hermitian? Normal?

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Q: erse of the given matrix

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Q: Q-7 (a) Express the matrix A defined by 1008 8 – 6i 1001 v17 – 8i 563i 2 + 3i A = 3+ 2i 786i as a…

A: For a matrix A we express it as a sum of Hermitian and skew Hermitian matrix A=P+Qwhere P=12[A+Aθ],…

Q: Q8. Find an invertible matrix S so that B = S-AS where () 1 A = B = 3 4 -1 -2 -3

A: Here B  =    3 4     -2 -3   Find eigenvalues of the matrix B|B-λI|=0    (3-λ)…

Q: Find the cofactor matrix of the following matrix 1 0 1 A = 4 -2 5 1

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Q: (b) Unitarily diagonalize the following matrix 3 -6i 6i 6 -

A: We have to diagonalize the given matrix A=3-6i6i-6 unitarily

Q: Find the elementary matrix E such that EB = A where %3D 2 1 1 24 1 A = 4 --2 and B -12 -8 3 6. -8 3…

A: We will find the elementary matrix.

Q: Consider the matrix A= 4 Find A-5A+31, where I, is (2x2) identity matrix 0. I. I. II 0 2 IV. V.…

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Q: Quèstion 12 1 0 Find a matrix P such that P- 2 3 0 3 P = OA. 1 P. 0 1 B. 1 0 C. 1 1 10 OD. 1 1 0 P.…

A: To find the matrix we have to find eigenvalues and corresponding eigenvector. Here with the help of…

Q: Identify the Hermitian matrix 1 -2i 2 -7i 9i (a) 0. [2i 1+ 2i 3i 1+i (b) 7i 2 1- i 1– 2i 3 2 + 3i 6.…

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Q: (BH) Recall that a matrix Q is orthogonal if Q' Q = I.

A: Given, A matrix Q is orthogonal if QTQ=I Proof: (a) The one way to write the norm for vector x is…

Q: Find a formula in terms of k for the entries of AK, where A is the Hermitian matrix below 13 4 9. 9.…

A: Here , A=-139-49+2i9-49-2i9-149 The characteristic equation of A is…

Q: Find the change-of-coordinates matrix from B to C. Find [x]c for x = - 2b, +4b2. Use part (a). %3D

A: Transition matrix

Q: 5. Find the cofactors and the adjoint matrix of A where (1 1 -1 b) A =|2 3 7 0 -1 a) A =-2 0 -2 4 -3…

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Q: find the cofactors of the matrix 1 21 3 4 C11= -4 C12= 3 C21= -2 %3D C22= -1 C11= -4 %3D C12= 3 C21=…

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Q: Let B={ 3 and = are bases for R². (a) Find the change-of-coordinates matrix from B to 5. (M) If [x],…

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Q: A. [oa] a) Let A = 0 4 Find a find matrix P) diagonal matrix D so that PAP=D for some invertible…

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Q: Find all (a) minors and (b) cofactors of the matrix.

A: Given- 1234 To find- all the minors and co factors of the above matrix. Concept used- For the minor…

Q: Quèstion 6 T(x, y, z) = (3x-4y, 5y+z), then the standard matrix of T is O[3 5 4 -1 3 4 5 -1 None 34…

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Q: 13. Find the cofactor matrix and adjoint of matrix A A = 2 -2 1 3 1 3

A: The given matrix is A=3-2121313-2. The main objective is to find the cofactor matrix and adjoint of…

Q: 4. Let u E R". Can you find a matrix A E Mmæn (R) so that Au = u for all u ER"?

A: For the solution follow the next step.