state if the given function is linear. If it is linear, find a matrix of that linear map with respect to the standard bases of the input and output spaces. If it is not linear, provide an example of an input that fails to follow the definition of being Linear.

Q: Evaluate det (A) for the matrix A=($ 2).

A: Given matrix is A=8254 The task is to find the inverse of the given matrix.

Q: Find a non-zero 2 x 2 matrix such that Note: 4890 -7 -67 28 24 =

A:

Q: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: Fill in each matrix for diagonalization of the matrix A = A = PDP-1 3 Ex: 5 30 1 4 -6 19 1 1 IG

A: We have to fill in each matrix for diagonalisable of the matrix.

Q: real matrix which is not diagonal. If (A + I)² = 0,

A:

Q: Represent the given information using relevant matrices

A: Labor Matrix:Rows represent the days of the week.The first column represents the number of hours…

Q: Assume that T is a linear transformation. Find the standard matrix of T. TR² R² first reflects…

A:

Q: Create a 2 × 2 matrix with the components -1, 1, and 0 such that when you multiply the matrix with a…

A: The reflection across x-axis means the matrix transforms one vector (x,y) to the vector (x,-y).

Q: 1 1 4 1 2] 01 21 1 0012 -1 0 0 2 1601 D) Find the rank of the matrix 0 1 2

A: