6. 1+i 3- 2i -6i 2i 4- 3i What is the trace of matrix A = 8i -1+i 5 6+ 3i O A) O B) 6+ 10i O 9 6+i O D)

Q: Find the elementary matrix E such that EC A where [2 4. 2 -1 2. -2 and C = 4 A 2 -1 -2 8 -6 [16 10 E…

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Q: 30: If reflection about origin is represented by the matrix R reflect the letter %3D ro 4 4 1 1 01…

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Q: Find the elementary matrix E such that EB = A where %3D 5 4 1 ] 4 1 A = |4 |7 -6 1 -1 and B = |12 3…

A: EB=A multiplying with B-1 on both sidesEBB-1=AB-1E=AB-1

Q: The mist Consider ann x m matrix A. Find dim(im(A)) + dim(ker(A")), in terms of m and n.

A: Please check step 2 for the solution.!

Q: 2. Prove that: k(4+ mB) - kA+(km) B for any mx n matrices A and B, and scalars k and m. (You may not…

A: 2 We have to prove that kA+mB=kA+kmB Where, A and B are m×n matrices and k and m are the scalars.…

Q: Show that if B is an n × n matrix with entries in C and  B3=B then B is diagonalisable. Where C is…

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Q: 1 4 Compute -u, where u = u•u 3 1 u•u (Type an integer or simplified fraction for each matrix…

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Q: B = . and = If X is a matrix that Let A = satisfies: Al, = 2B – XC. Then X is %3D

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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: 4. Find the cofactor matrix for the matrix. 5 9 1 8 5 6 4

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Q: a) Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

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Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: b) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s)…

A: Negative definite: A square matrix is said to be negative definite if all the eigenvalues of the…

Q: 4. Prove that det (A) = det (A¹) for a 2 × 2 matrix.

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Q: State Cayley-Hamilton theorem and prove this for following matrix [1 1 A 1 2 -1 %3D [5 8

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Q: '(Suppose) 31 [2 A = |3 [4 4 2 4 3 2] The minor and cofactor of the entry a,3 of the matrix A are...…

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Q: Please find the question attached.

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Q: 4. Decide if there is a three by three matrix A such that A. 1 for all æ, y, z in R.

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Q: The Matrix B from 3 x 2 at b = 1- - is %3D 1. 2. 3.

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Q: Show that A satisfies its characteristic equation. That is, A2 − 5A + 6I2 = 02. (This result is known…

A: Question is- Show that A satisfies its characteristic equation. That is, A2 − 5A + 6I2 = 02. (This…

Q: (b) Explain why in general, if u = [u uz] is a row of length 2, A = a1,1 a1,2 [@2,1 @2,2] we always…

A: Answer

Q: 3) Identify the element in the matrix. [O 2 4 6 X =0 3 6 9 0 48 12 X2,4 =h X3,2 %3D X3,4 %3D

A: NOTE: Refresh your page if you can't see any equations. . the element at the second row and fourth…

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

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Q: Let Q and Q' be two equivalent quadratic forms with respective n x n matrices A and B. respectively.…

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Q: 5. Calculate the L and U matrix and proof that PA=LU. 10 -7 0 A = -3 26 5 -15

A: Firstly I find lower triangular matrix LL and an upper triangular matrix UU And the show that PA=…

Q: Illustrate the Gersgorin theorem by the matrix 2 1+ 2i 0 A = -1 -2 – 2i 1/4 1/41/2 140 12 1/7 1/2…

A: We state the theorem and explain it with the help of the given matrix A.

Q: Suppose that A, B, C and D are n × n matrices satisfying the equation ABC = D. Show that if DA is…

A: Given:Suppose that A,B,C and D are n×n matrices ABC=DInvertible matrix:A square matix is invertible…

Q: نقطة واحدة Show element equal to 18 in the * matrix Y Y= 2 5 7 4 8 3 10 20 30 12 14 16 18 Y(18) O…

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Q: • The Matrix B from 3 × 2 at bj = 1 - is го 1. 2 2. 7 3. -1 4. 1 1 -2 2 3 4

A: concept of matrix  bij=1-i/j , the entries of matrix B is b11,b12,b21,b22,b31,b32

Q: Given Pauli matrices X,Y, Z ; show that X2 = Y2 = Z² = 1 (a) by using the matrix representation (b)…

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Q: Use Proposition 2.50 to state Jacobi's method and the Gauss-Seidel method in matrix notation for the…

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Q: Suppose CA = I, (the nxn identity matrix). Show that the equation Ax = 0 has only the trivial…

A: Let A be m×n matrix then Rank(A) + Nullity(A) = number of columns of A Where Rank(A) is the…

Q: 1. Show that matrix A is singular 1 2 A= 3 -1 -2 3 -2

A: Given  A=1203-12-23-2

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: 18. Let A be a 3 x 5 matrix with 2 pivots. What is the dimension of Nul(A)?

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Q: [1 Let A = 2 and V = |1]. What is the sum of the entries of the B = %3D 14 5 1 matrix VT (AT — (А -…

A: We have to find sum of entries of given expression.

Q: 10. Assuming that all matrices are n x n and invertible. Solve for A (CDF ACB-C = D¯ B-'C EP Type…

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Q: 3 3 , Let M 1 -2 -3 Find c1, C2, and C3 such that M3 +¢¸M² + c2M + C3I3 = 0, where Iz is the…

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Q: Given that A and B are 5 x 5 matrices and B is invertible. If det(BAB-1 – 21;) = 7, where %3D Iz is…

A: Let's find.

Q: (b) Find the matrix representation [J]Bn+1,Bn• ght as Mon onas hUiver Unn mersi niversi ash ve

A: The given question is related with linear transformation. Let n ≥ 1 be an integer , and let J : Pn →…

Q: 2 Suppose A = is positive semi definite matrix then: 10 O a. a < -V20 O b. a = ±v20 O c. lal < 20 O…

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Q: A be square matrix. I f A"= Onva for %3D n> 2. Then A= Onen

A: Suppose A be any square matrix of order n such that An=On×n     for n&gt;2

Q: Show that it is impossible to find two real 2 x 2 matrices A and B such that AB - BA = dI where d…

A: Take A and B are arbitrary matrices and find AB-BA and analyse the diagonal elements

Q: 2. Compute the matrices D, P such that D =P-'AP. Verify the equation holds. [7 5 0 A 1 0 1

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Q: hatate the following triangle uith Q= 45° by the accemate diagram and I final matrix 12 C50,50)…

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Q: a) Prove that the matrix A = is diagonalizable if –4bc (a– d)². What happens when –4bc = (a– d)² ?

A: Given,         A= abcd

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

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Q: Write down what it means for a n x k matrix to be singular.

A: As we know, If matrix is singular then it has determinant equals to '0' For Finding determinant…