Suppose A is a 2 x 2 matrix such that A and 1 A What is A-1?

Q: Let G be a 2x2 matrix with a and b in the top row and 0 and c as the bottom row, where a,b,c are…

A:

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

Q: A? 0 0 A =

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: Q2] a) Write each (PRODUCT) of the following as a single matrix: i -17 2 -2 -1]-i -2 5] -2| -1 1 -1]…

A:

Q: 2. Determine the zeros and poles of the recursive equation below. y[n] = x[n − 1] − 2x[n - 2] + 2x[n…

A: Solution : Z transform of delayed function: Ƶ(x(n-a))=z-aX(z) Given equation is,…

Q: Show that A and B are not similar matrices

A: Given matrix is The characteristic polynomial of matrix A is

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: Let A and B be two square matrices of the same size. Prove that det(AB) = det(BA).

A: Using Determinant and elementary row operations,

Q: Show that any 3 × 3 matrix of the form ⎧ ⎩ a 1 0 0 a 1 0 0 b ⎫ ⎭ is defective.

A: We have to show that given matrix is defective.

Q: Show that A and B are not similar matrices

A:

Q: For A 3 1 N² = A. 2 find a 3 x 3 matrix X such that

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: Find the matrices of x and y if. 2x- y = [ -6 3 2 I and x+2y = 1

A:

Q: Let A and B be similar matrices Show that if A? = A then B = B.

A: Two matrices C and D are said to be similar matrices if there exists a non-singular matrix P such…

Q: Let A be an m × n matrix. Under what circumstances will ||A||2 = ||A||F?

A:

Q: -3 -1 Find all a so that the matrix A = 1 -1 is positive -1 4

A: Matrix A is position if and only if all of the leading principal minors are positive.    Then follow…

Q: If A is a 1 x 2 matrix and the sum A + B can be computed, what is the dimension of B? X

A:

Q: If A is a square matrix whose diagonal entries are all zero, then detA = 0.

A: Given information: A is a square matrix whose diagonal entries are all zero.

Q: If A is a square matrix such that some row of A2 is a linear combination of the other rows of A2,…

A:

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 matrix A is such that, 3A³ + 2A² + 5A + I = 0 then its inverse is?

A:

Q: [2 Let A = Find all matrices of the form B = that commute with A. P In other words find all matrices…

A: We have to do both the matrix multiplication.

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

A: Using the properties of determinants

Q: Given a matrix A = for what conditions on a, b, c, and d will the matrix not have an inverse?

A:

Q: Prove that An nxn matrix A is non singular if and only if it can be written as a product of…

A: We prove that an nxn matrix A is non singular if and only if it can be written as a product of…

Q: Determine the dimensions of Nul A and Col A for the matrices. A =

A:

Q: (2v² + 4u²v)du + (4uv + 3u³)dv = 0

A:

Q: Let A be a 3x3 matrix. Show that det(A) = 0 if and only if the columns of A are linearly dependent.

A: Let A be a 3 * 3 matrix. We are to show that det(A) = 0 if and only if the columns of A are linearly…

Q: Compute for the Inverse of Matrix A A=1 2 3 4 A BI E =

A: Given matrix is A = 1234

Q: Let 0. A = |0 -11 -6 1 Write A as a product of elementary matrices. 2. 4)

A: