Let B = {1+x, 1 – x², x + 2x²} and p(x) = 7+ 10x + 11x². You are given that B is a basis for IP2. %3D Ir [p(x)]g = then the value of B is

Q: Find the change-of-coordinates matrix from B to the standard basis in R². -5 1 •(3][4]} - PB B= -188…

A:

Q: . Let T₁ ([x2]) = [-2x₁ + 7x₂) + Find the matrix A such that T.(T.(X)) = AX ¹2 ([x2]) = [2x + ⁹*²].…

A:

Q: 2. Write the following in vector/matrix notation, specifying all components of the matrices. If it…

A:

Q: two

A:

Q: Given the matrix 9. 6 -1 -5 -3 -4 A = 3 -6 -5 1 -3 Find an invertible matrix P so that J = P-AP is…

A:

Q: Find an invertible matrix P such that: 2 -2 1 P-1 -1 3 -1 P 100 2 -4 3. 0 0 6

A:

Q: If Y and Y are the first and last column vectors in the inverse of a [1 -1 2] matrix A = 0 3 2 then…

A:

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

A:

Q: Let 0 9. A = = [6 0 Is it possible to find a two by two real matrix B such that A = eB₂

A:

Q: Let A, B and C be invertible, nxn matrices with AB BA and I, the n x n identity matrix. If AXB-= I+…

A: Invertible Matrix: An invertible matrix is a matrix for which matrix inversion operation exists,…

Q: Suppose A is a 2 x 2 matrix. Show that the constant term of the characteristic equation |A – XI| = 0…

A: According to the given data, shows that the constant term of characteristic equation is equal to…

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

A:

Q: Compute (a) llAll2 and (b) cond2(A) for the indicated matrix.

A: Given matrix: A=01102-2 To find: ||A||2  and cond2(A)

Q: 2a. Write a MATLAB command that creates a row vector u that has the elements: Cos 3e 19π -2e, log10…

A: 2a. We write MATLAB command that creates a row vector u. Then we will find the maximum value of…

Q: EXER 7: MATRICES Prove that if N is invertible then MN¹ = N¹M if and only if MN=NM.

A:

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: Let A be an nxn matrix. Prove that dim(col(A²)) < dim(col(A)).

A: Given: Assume that, A is an n×n matrix.

Q: Set up the matrix which will perform the following transformation and write down its character. (x…

A:

Q: Find the transpose of the resulting matrix: -100 A = 2 3 4 x 5 2 5-4

A:

Q: Find the change of basis matrix [B]. {0}{000) C = B = -2 -3 2 -2 -31 2 4 5 -3

A:

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

A:

Q: Let C be a 6x6 matrix with. real eigenvalues -1, 2,4 and no complexores. Write the characterstic…

A:

Q: Write f= x + 10x1x2 + x3 as a difference of squares, and f= x? + 10x,x2 + 30x as a sum of squares.…

A: Given f=x12+10x1x2+x22.  Let the associated matrix of f be A=abba is 2×2 symmetric matrix. Then,…

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

A:

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 7A +…

A:

Q: Consider the quadratic polynomial q(x) = 2x + 8x1x2 – 8x – 3x1 – 3x2 + 3. - - Find the symmetric…

A:

Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A:

Q: 4. Consider the same function f(x) = xe" again. Now, we are going to find the interpolating…

A: