Mark each statement True or False, and justify your answer. a. If A is an n× ʼn matrix, then det(kA) = k det A for any real scalar k . b. If the rows of the matrix A are linearly dependent, then det A + 0.

Find the inverse matrix. Must show work and label each step as a linear combination of row transformation (example: -R1+R2) or unchanged.

Determine whether or not the given matrix A is diagonalizable. If it is, find a diagonalizing matrix P and diagonal matrix D such that P AP = D. 300 030 022 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrix is diagonalizable, {P,D) = . (Use a comma to separate matrices as needed.) OB. The matrix is not diagonalizable.

Solve the equation for the variable C. Assume that the dimensions are such that matrix multiplication and addition are possible and that inverses exist when needed.   CZ=Y