If A is a 2 x2 matrix such that det A) = - 3 and tr(A) =5 then the characterestic polynomial of A is p) =x2 -5A-3

Q: Find x such that the matrix is singular. A = -3 -2 X =

A: Given A = 6x-3-2

Q: A? 0 0 A =

A:

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: If A is a 2 × 2 matrix, prove that the characteristic polynomial of A is χ(λ) = λ2 − (trA)λ + (det…

A:

Q: Find x such that the matrix A is equal to its own inverse.

A: We have A=-2-33x Now, A-1=1AadjA For a 2×2 matrix A=abcd, we have A=ad-bc  , adjA=d-b-ca Hence, for…

Q: Find an orthogonal matrix P that orthogonally reduces the quadratic form Q(x) = x" Ax sa} + 3.x3 +…

A:

Q: For matrix A and a scalar k, (kA)T is equal to: k(A^T) k(A) (k^2) x (A) (k^2) x (A^T)

A: We will solve the matrix operation.

Q: Find the symmetric matrix A associated with the given quadratic form. 2x2-3y2-z2-4xy

A:

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: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: If A 0 is a square matrix, then A is invertible.

A: Given: Any square matrix A≠0 Assertion: If A≠0 is a square matrix, then A is invertible. To prove:…

Q: .1 Suppose A is a matrix with characteristic polynomial CA(x) = x²(x – 1)³(x+2)². Determine the…

A: The solution are next step

Q: A" A is invertible if and only if A has linearly independent columns.

A: ATA is invertible if and only if A has linearly independent columns.

Q: Find the characteristic polynomial of the matrix 3 -5 A = 1 -2 -5 3 2(x) =D

A: Given,            A=3-5001-2-530

Q: Find the characteristic polynomial of the matrix 4 5 0 A = 4 3 -4 4 0 p(x) =

A:

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given:0111 over ℤ2

Q: Let P be an m × m matrix with entries in the polynomial algebra F [x]. L:1.1.

A:

Q: Find x such that the matrix is singular. A = -3 -4 X =

A: Matrix is said to be singular , if and only if the matrix has determinant is zero Det(A) = 0

Q: Find the characteristic polynomial of the matrix -9 A = 1 p(z)

A:

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: To: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). a001a001a

Q: If A is a 2×2 matrix such that trace(A) = det(A) = 3, then %3D value of trace of (A-!) ?

A: Introduction: It is the sum of the diagonal elements of the matrix from upper left to lower right.…

Q: Consider A and B are two square matrices and B is a scalar. Calculate (BA^T B)^(-1) = * \beta…

A: Topic:- matrix operation  Note:- if more than one question uploaded than only first question need to…

Q: (b) triangular with l's on its diagonal, and U is upper triangular. Use the results in (a) to obtain…

A:

Q: (b) Find a real symmetric matrix C of the quadratic form: Q(x1,x2,x3) = xỉ+4x3+6x3+2x1X2+x2x3+3x1x3.…

A:

Q: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: ^ = [1 ] A If A is diagonalizable, find an invertible 2 x 2 matrix P and a 2 x 2 diagonal matrix D…

A: Given that the matrix A=0-440. If the given matrix is diagonalizable , find an invertible matrix and…

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: Suppose A is a 2 × 2 matrix, where -2 | u = Au = -4 A?u = 4 A³u 2 20 – 20 – 10. The minimal…

A:

Q: a. Suppose the vector x = and the symmetric matrix A = Show that for the quadratic form Q(x1,x2) =…

A:

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1] A…

A: NOTE:We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If A is a 2 x2 matrix such that det(A) = -3 and tr(A) = 5 then the characterestic polynomial of A is…

A: For a matrix abcd the characterstic polynomial is λ2-tr(A)λ+det(A)Given tr(A)=5 and det(A)=-3

Q: Let A be 2 x2 matrix with tr(A)=4, det(A)=5,then the characteristic polynomial of A is: Select one:…

A:

Q: Let 4 1 -2 2 1 A = 1 -2 0 3 -2 2 1 -2 -1, Use Householder method to transform A into a tridiagonal…

A:

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

A:

Q: Let A be a 4 × 4 matrix and suppose that A is a diagonalizable. If the characteristic polynomial of…

A:

Q: Let A be an m X n matrix with linearly independent columns and let A = QR be a QR factorization of…

A: Let A be an mxn matrix with linearly independent columns. The columns of matrix Q in QR…

Q: If A is a positive definite matrix and B is positive semi-definite, show that trace (AB) 2 O with…

A:

Q: Let A be a symmetric 2 X 2 matrix and let k be a scalar. Prove that the graph of the quadratic…

A:

Q: 2. Write the quadratic function f(x,,y;)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) =…

A:

Q: Let A = (a;;)ij be an m x n matrix of real numbers, and let f : R" Rm be defined by 0-0 x2 x2 f = A

A: To find the derivative of f given: matrix A which has m rows and n columns  also the function f…

Q: Find a 3 x 3 matrix A such that Aa = 9x for all a in R³

A: We have to find matrix A such that Ax = 9x

Q: If A is a 2 x2 matrix such that det(A) = -3 and tr(A) = 5 then the characterestic polynomial of A is…

A:

Q: Find the symmetric matrix A associated with the given quadratic form.

A: To determine: The symmetric matrix A associated with the given quadratic form. 5 x12 - x22  + 2 x32…

Q: Find x such that the matrix is singular. x 5 A = -3 2

A:

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

A:

Q: Find c such that the number of the pivots to the matrix below is 2: 1 1 1 -1

A:

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists)

A: Given a matrix, Let A=0111 over Z2 To find the inverse of A.

Q: 1. Let f(r) = ar +bx² + cz+d be a polynomial such that f(1) = 0, f(-1) = 12, f(2) = 12 and f(-2) =…

A:

Q: What is the det(A)if a matrix has p(A)=A5 - Aª + 2A3 +A² + A_as its characteristic polynomial. O A.…

A:

Q: Find the characteristic polynomial of the matrix -3 1 A = -3 -1 -3 -4 p(x) =

A: Given problem is :