k= M = 3 -9 13+ k -4 -4 13 16 21 -24

Q: Let A be a m×n matrix. Prove that AB and Ba both exist only if B is an n×m matrix.

A: Explanation of the answer is as follows

Q: Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the proper…

A: Step 1: Step 2: Step 3:

Q: A? 0 0 A =

A:

Q: Let A and B be 2x2 matrices such that B is invertible If detA)2 and det)-, then detA'e) Select one:…

A:

Q: Find the null space of the following matrix: A= [( 1,0,2,),(0,1,1),(0,0,0),(0,0,0)]

A:

Q: Find a matrix A such that 5 ¹0-08-08-0 A 5 A A = A =

A: We can solve this as follows:

Q: Let A and B be n x n matrices. Their product, AB, is singular. Show at least one of A or B must be…

A: Let A and B be n×n matrices such that their product AB is singular.We have to show that at least one…

Q: Let A and B be n X n matrices with A∽ B. A is invertible if and only if B is invertible.

A:

Q: Let A be any invertible 9 x 9 matrix. Which of the following is equal to det(Adj A)? OA. (det A) B.…

A: Given: A is an invertible matrix of order 9×9 We are required to find: det(AdjA)

Q: Let A = 3 ů 5. positive definite show that the matrix A is. پول و مع دول ۷۵

A: A matrix is said to be positive definite if the given matrix is symmetric and all its eigen values…

Q: Let A be an m x n matrix, and let B be an n x m matrix. Show that if m > n, then AB is not…

A:

Q: Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that PTAP gives the proper…

A:

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: Get a base for your null space. Indicates which dimension it is in. The matrix is shown in the…

A: Step 1:

Q: + 3 [x+y__z+3] = 0 ly – 4 z+w

A: Consider two matrices A and B. These two matrices are said to be equal only if they have the same…

Q: Find a 3 x 3 matrix A such that Az = 10 for all i in R³. A =

A: Given Ax=10x  We have to find 3×3 matrix A  Now

Q: Find a matrix X such that AX=B 0 6 A = [²2 -B = [1 2 ] 91 L7 8. 4

A: Given that we have to find a matrix  .Obviously order of the matrix  is .Let Now so  ,

Q: If A is square matrix of order 3 such that|3 A| = 54. Find |A|

A: Using the properties of determinants

Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: Let a be a real number. Let 1 1 A = | 0 1 1 1 1 2 a) Find the value of a for which the matrix is not…

A:

Q: Show that if A is an m × n matrix such that AAT is non- singular, then rank A = m.

A: Let AAT can be non singular only if the columns in A are linear independent and they span the column…

Q: e a square Fits diagona diagonal ele anal the val

A:

Q: Determine a matrix H such that H¹MH is diagonal or Jordan: (2 0 1 0 0201 0020 000 2, M₂1

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Q: TF A 5 x 8 matrix cannot have a 2-dimensional null space.

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Q: Let T(x) = Ax for the matrix A and [4 -4 -16] -16, b = A = 7 5 Lo 0 1 1 Select true or false for…

A: Given that  A=4-4-1675-16011, b=3-11, c=-451 Select true or false statement.

Q: What is the null space of this matrix:   A = 3 0 0 2 0 0 1 1 1

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: