Find the examples that satisfy the statement in the given items and show some work how they are correct examples (a) A 4 x 4 matrices A that is not digonalizable. (b) (c) Two matrices A and B that have the same characteristic polynomial but are not similar. Two diagonal matrices D₁ and D2 that are similar but they are not equal.

Q: A B Let m and n be whole numbers. Matrix P is of order/size m x n. Matrix Q is of order/size n x m.…

A: Given that, m and n are whole numbers. Matrix P is of order m×n and  matrix Q is of order n×m. Want:…

Q: Multiply matrix [1 2 3] by [5 4 2 030

A:

Q: list 2 matrices that commute with all n x n matrices

A: Scalar matrix is the only matrix which commute with all matrices   Let A=kI is a scalar matrix ,…

Q: Describe matrix multiplication of two matrices A and B in terms of linear functionals (the linear…

A: Solution:-

Q: Suppose that matrix A has dimension 5•3 and that matrix B has dimension 3•5. Decide whether product…

A: Given: The matrix A has dimension 5×3 and that matrix B has dimension 3×5. To Find: To decide…

Q: Explain the fact “Cofactors are useful when matrices have many zeros”.

A:

Q: Determine all 2 × 2 matrices A such that AB = B A for any 2 × 2 matrix B.

A: Let A=abcd and B=pqrs be any 2×2 matrices.

Q: 2. Assume that all the operations are properly defined, solve the following equation for the unknown…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Prove using elements that for any square matrices A,B of the same size and constant K.…

A: For any square matrices A,B of the same size and constant K.  tr(kA+B)=ktr(A)+tr(B)

Q: If A is an nxn matrix, then the equation Ax = b has at least one solution for each b in R".

A: (C)

Q: Find the LU factorization of the matrix: A = 1 2 0 -1 -1 3 4]. 3 -2 -8 2 Show all the steps of your…

A: Answer is given in below stepsExplanation:Step 1: Step 2: Step 3: Step 4:

Q: Find matrix such that 5 3 -1] X+ 2 -3 1

A:

Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: For this exercise assume that the matrices are all nxn. The statement in this exercise is an…

A:

Q: 3 4 Let X and Y in the set of 2 × 2 matrices, M22. %3D -11 2 3 Determine whether A = or B are in…

A: Given  X=2-121, Y=34-11 and A=0-1181, B=2312

Q: () Write the statement of Cayley-Hamilton theorem for square matrices.

A: Cayley-Hamilton statement

Q: 3 |2 -3 -47 Гз -17 The matrix product 2 4 5 |0 1 1.

A:

Q: Show that any positive definite square root of a diagonal, positive definite 2 x 2 matrix must also…

A:

Q: 6. Let A be a 2x 2 matrix such that (a) The above equations can be written in the form A -1 0 -1 0 B…

A: The objective is to find the matrix B. heck whether the matrix B is diagonalizable or not and also…

Q: Can you please help with finding an inverse of an elementary matrices?

A: An elementary matrix is a kind of matrices that differ from the identity matrix from a single…

Q: For this exercise assume that the matrices are all nxn. The statement in this exercise is an…

A: Given that if the equation Ax=0 has only the trivial solution then A is row equivalent to the n×n…

Q: Is the following matrix diagonalizable¹? 3 B=0 0 -3 1] 3 1 0 3

A:

Q: 4, 4, -7 -5 Compute 2(2A - 3B) if matrix A = and matrix B = %3D 3 - 4 2. 2(2A - 3B) = (Simplify your…

A: Multiply A by 2A=433-42A=2433-42A=866-8Multiply B by -3B=-7-52-4-3B=-3-7-52-4-3B=2115-612

Q: Construct a 3x5 matrix A such that dim Nul 4. Explain and justify your answeT.

A: We need to construct a 3x5 matrix A such that dim Nul A = 4. So, nullity(A) = dim Nul A = 4. We know…

Q: 2 B= [11] 3 -1 Write B and B-¹ as products of elementary matrices.

A:

Q: 7. 2 1 -1 2 Matrix + 2 Matrix -1 3 11

A: Topic:- matrix addition

Q: = [2 1 3 -1 -1 -1 2

A:

Q: The matrices [2 1/2 1² 1] and [33 }] are row equivalent. -1 0 -2 LO A True B) False

A: Given matrices are 1-10211and 301031 Now find the given matrices are row equivalent or not:

Q: If A + 0 and B+ 0 are square matrices of the same order, then AB + 0.

A:

Q: IA - (34) and B- (-5 8 -2 (a) (AB) (b) BTAT 10. f -5 find

A:

Q: Q5 Let -1 7 A = 1 15 -2 (5a) Find a 3 x 3 matrix P and a diagonal matrix 0 0 D= such that A = PDP-1…

A:

Q: Explain why det (BPB¯¹) = det(P) for any matrices P and B. Assume both sides of the equation are…

A:

Q: How " Same" types of 3 by many matrices in reduced roW-echelon form are there ? a)2 (b)3 (C)4 (d)5

A: The objective is to find how many type of 3×1 matrices in reduced row echelon form are there. The…

Q: Pleasev don't provide handwritten solution ....

A: The LU factorization of matrix A is A = LU, where:∙  L=⎣⎢⎡​1−1−1​011​001​⎦⎥⎤​∙…