4. Let 1 A = 8 -1 -1 -4 1 -1 Prove that A is not diagonalizable over R, but is diagonaliz- able over C. (b) Find an invertible matrix X € M3x3(C) such that X-'AX is diagonal.

Q: If A and B are two n x n invertible matrices, then one of the following is always correct a) (AB)T =…

A:

Q: B) Suppose A is an invertible matrix inM, (R). And x, y E R". Prove it: det(A+ ry") = (1+y"…

A: Given: A is an invertible matrix in Mn(ℝ) x,y∈ℝn To prove: det(A+xyT)=(I+yTA-1x)det(A)

Q: Matrix [1 3 4 in Z5 is digonalizable. True False

A:

Q: if A is (m*n) matrix, prove 'rank(A)=n-dim(N(A))

A:

Q: Ax = b has exactly one solution for every n*1 matrix b, then det(A) # 0

A:

Q: 2) An n x n matrix A is called nilpotent if Ak = 0 for some positive integer k. Show that if A + 0…

A:

Q: The maximum value of the determinant among all 2×2 real symmetric matrices with trace 16 is

A: But they cannot be both negative as a+d=16 And the value of ad is maximum  a=8, b=8 Therefore

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: 17. Is Identity matrix Idempotent? (yes/no) 18. Which Matrix has no inverse matrix?

A: An idempotent matrix is a matrix which when multiplied by itself results in the matrix itself. An…

Q: If A is a matrix, what will the following commands display? (Explain them) [m,n]-size(A), inv(A),…

A: 1. A(:,j) will display the j-th column of matrix A. The : symbol in the command represents all the…

Q: (31/1/2 03 A= 1 1 - 1 3 3 3 1 0 0 0 0 0 0 0 -130 0 0 10 3/

A: According to the given matrix A, find an invertible matrix P such that .

Q: What is a singular matrix

A:

Q: 29. Let the characteristic polynomial of a matrix be p(2)= 2² +62+9. a) What are the dimensions of…

A: We have to solve given problem:

Q: If matrix A is invertible, then A admits an LU (or LDU) factorization if and only if there are no…

A: Proposition Let be k*kmatrix. If can be reduced to row echelon form by Gaussian elimination without…

Q: Let -3 4 A-[ 3³ -1], E-[42], F-[^2} = = = -5 Compute the indicated matrix. (If this is not possible,…

A:

Q: Let A, B, and A+B_ all be square invertible matrices of the same size. Show that (A +B')' = A(A+B)'…

A:

Q: 26) Let A be annxn matrix such that A2 = 0. Then what can we say about the matrix I+ A? A)I+ A is…

A:

Q: Find the position of the particle at the first time is turns around. Find the total distance…

A: solution of the given problem is below...

Q: ГО 5 4 5 1 2 2 3] A = [1

A:

Q: An upper triangular matrix A is one whose entries a^ij are zero if i > j. Prove that the product C =…

A:

Q: 3. Find all matrices which satisfy the matrix equation (::)(; })-(; :)(::)

A: Here,

Q: There exists a 7 x 6 matrix A with rank(A) = nullity(A). A) True B) False

A: Suppose that A  be  the  matrix of size 7.Recall  Rank-nullity theorem:  Let  A   be  a  matrix  of…

Q: 4. Diagonalize the matrix, if possible. That is, find an invertible matrix P and a diagonal matrix D…

A:

Q: 2. a) A, BEM₁ (12) komutatif ters-simetrik AB matriinin simetrik dkup olmadı. matris ise gını…

A: Let A be a square matrix,  then If AT=A , then A is called symmetricIf AT=-A , then A is called…

Q: Q1/ Give the mathematical interpretation for the following items ( enhance your answer with a…

A:

Q: Consider the matrix distributive property. (c + d)A = CA + dA, where A is a matrix and c and d are…

A: Given Property is (c+d)A=cA+dA where A is matrix and c and d are scalarsGiven A=[aij]We know that…

Q: Consider the non-singular (invertible) matrices A, B, and C, such that A = 9CB + B. With certainty A…

A: Given  We are given an expression in matrix form which is. A = 9CB + B Where all ABC are matrices

Q: Using the Rank-Nullity Theorem, explain why an n x n matrix A will not be invertible if rank(A) < n.

A: The Rank-Nullity Theorem states that for a linear transformation T:V→W between finite-dimensional…

Q: 3. Find the Jordan canonical form %]. 6 4 -69 (a) A= [- 1 241 1 2 (b) A= 4 5 (Ⓒ) A = [5 }]. -2 7

A: We have to find the Jordan canonical form of the matrix over ℂ. Note: There are multiple subparts.…

Q: 13. a) Show that if A and B are n x n matrices, at least one of which is invertible, then AB and BA…

A: (a) If A and B are two n×n matrices, and one of them is invertible, then show that AB and BA are…

Q: 3. If A is a nonsingular matrix, then A' is nonsingular and its inverse is (A')1 = (A') '. Prove it!

A: A matrix A is said to be invertible if and only if  det(A) is not equal to zero i.e.  |A| ≠ 0

Q: 8. Choose one of the following to complete. Extra credit may be earned if you complete both. a)…

A: Given that A and B is invertible. Then AB-1 exists. Also, AB-1=A-1B-1.

Q: Let A, B and A+B be invertible matrices of order n. Show that also A +B¯! is nonsingular and that =…

A:

Q: When a mxn matrix is invertible, is that mean that it's rank is n? Is that because invertible matrix…

A: First of all to be invertible, a matrix need to be square matrix. So first condition is m=n

Q: 5. Show that a complex square matrix is unitary if and only if it is unitarily equivalent to a…

A: