2. |- 3) Find the charactoristic equation of -2 2 -3 Verify cayley- Hamilton theonem hence Find the inverse of the matrix

Q: Complete the matrix A so that it is skew-Hermitian. i 2—6і - A = 1 9i Y = = 2

A: Given the matrix, A=0i2-6ix01yz9i The matrix A is said to be skew-Hermitian matrix if, A*=-A Where…

Q: Give a matrix representation of the quadratic form f(x, y, z) = 4x 2 + 9y2+ 16z 2 − 2xy + 4xz − 6yz…

A: Given: f(x,y,z)=4x2+9y2+16z2-2xy+4xz-6yz             We have to find a matrix representation of the…

Q: For the matrix A= 1 5 -i 8 7 9i 5i 2 3 B= 2 5 -i 8 3 9i 5i 5 3 Find 1- Transpose A* conjugate B 2-…

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Q: Find a formula for det(rA) when A is an n  n matrix.

A: Find a formula for det(rA) when A is an n  n matrix.

Q: 10.3 (a) Solve the following system of equations by LU decomposition without pivoting X1 +7x2- 4x3 =…

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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: Solve the following equations using matrix inversion. yi - y3 = 1 2y1 + 3y2 – y, = 1 yi - y2 - y3 =…

A: Given the equations are y1 - y3 = 12y1 + 3y2 - y3 = 1y1 - y2 - y3 = 3

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

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Q: Show AB + BA for the indicated matrices. A= 2 3] B = -1

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Q: For the matrix A , use the Cayley­Hamilton Theorem to compute A -1 and A -2 by expressing each as a…

A: According to Cayley Hamilton theorem, any square matrix satisfies its own characteristics.

Q: which of the following is the cofactor A13 of matrix?

A: Simply omit that raw and column whose co-factor matrix required and write rest all elements in same…

Q: Given matrix A, Find A-1 by forming [Al I] and then using row operations to obtain [Il B], where A-1…

A: Given, the matrix                       We have to find the inverse of this matrix. Also check AA-1…

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: 5.1) Find the matrix A if det(A) =2 and the classical adjoint is -1 - 2 ad j(A) = - 6 1 6. 24 4.

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Q: :- -b where a and b are positive real numbers, The matrix C %3D a V3 2 and C2. V3 2 m+n TC can be…

A: The given problem is to find the value of cos(π/12) that can be written in the given form using the…

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: Solve the equation (X – A)B = BC for X, assuming A, B, and C are all invertible (note that A, B, C,…

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

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Q: Prove that the quadratic equation A^2 - 3A = 2I hold true for the matrix A =  5  -6  -6        -1…

A: The detailed solution is as follows below:

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: Use A-1 =(1/detA)adj A to compute the in­verse of the coefficient matrix x + y = 1   x-y=2

A: x+y=1 x-y=2 We need to find the inverse using A-1 =(1/detA)adj A

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

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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: Find a formula in terms of k for the entries of A", where A is the diagonalizable matrix below. 4 -2…

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Q: 7 Q8. Verify Cayley-Hamilton theorem for the matrix A = 5 and hence find its -4 -3 inverse.

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Q: [1 A 2 1 0 and b : 3 2 3 Jse Gauss-Jordan elimination to compute the inverse of the matrix

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Q: Given a matrix A = for what conditions on a, b, c, and d will the matrix not have an inverse?

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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: Solve x, y, z, w using Matrix Inversion 3X +5Y+92 =13 54-92+3W =50 = -50 3D13 3W - 2X -5y

A: To solve x, y, z and w using matrix inversion.

Q: -2 1 To show that the matrix A = -1 1 satisfies its char- 1 -3 2

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Q: 19. Verify that the matrix is orthogonal, and find its inverse. 3 25 12 16 25 25 ... bp 云 41535 45

A: Solution:-

Q: Reduce the quadratic form x2+y²-9xy into a canonical form of the matrix.

A: The given equation is x2+y2-9xy. The standard equation is ax2+by2+cz2+2fyz+2gzx+2hxy. The…

Q: if the chractrestic polynomial of a matrix A is p(^) = (^ +1)(^ - 2)2 then det(-A) +tr (A) = 1 7 -2…

A: As we have 3 roots of characteristics polynomial.

Q: With x and y as in your answer to question 3, the matrix

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Q: Given the matrix -3 -1 1 4 1 -2 1 A = 3 -3 1 -2 -1 0 -3| Find an invertible matrix P so that J =…

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Q: 2] find 1 -1 3 - If A = and B 1 |3| -2 (а) ЗА — В. - (b) The matrix X such that 3A – B+ 3X = 0. ||…

A: As per guideline we have to solve only three parts

Q: Let M = -3 Find c and c2 such that M² +cqM+c»I½ =0, where I, is the identity 2 × 2 matrix and 0 is…

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Q: -2 1 -1 1 -1 1 3 (a) does the inverse of the matrix exist? Your answer is (input Yes or No): Are the…

A: The inverse of a matrix is said to exist if and only if the determinant of the matrix is non zero. A…

Q: 1 Use the formula A- = -b to find the inverse of the 2 x 2 matrix, if possible. (If an answer does…

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Q: Find a formula in terms of k for the entries of Ak, where A is the diagonalizable matrix below. -3 8…

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Q: 10. Find the simetric matrix for the quadratic form Q(x1,x2,x3) = xỉ + 3x + x,x2 – x1x3

A: Since you have asked multiple question, we will solve the first question  for you. If you want any…

Q: Use the matrix capabilities of a graphing utility to find the inverse of the matrix (if it exists).…

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Q: Find all possible choices of c that would make the following matrix singular:

A: For a singular matrix, the determinant value has to be equal to 0. |A| = 0

Q: Find all a and B >0 so that the matrix B = 23 6 2 is diagonally dominant;

A: A square matrix is diagonally dominant if   for .

Q: Find x such that the matrix is singular.

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Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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Q: Find all a and B> 0 so that the matrix 4 a 28 5 4 2 is strictly diagonally dominant.

A: In a diagonally dominant square matrix, the magnitude of the element corresponding to the diagonal,…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.