3 Each year, 20% of all untenured State University faculty become tenured, 5% quit, and 75% remain untenured. Each year, 90% of all tenured S.U. faculty remain tenured and 10% quit. Let U, be the number of untenured S.U. faculty at the beginning of year t, and T, the tenured number. [U+1] Use matrix multiplication to relate the vector to T++1] the vector

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

A:

Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

A:

Q: 1 −1 1 -2 1 2 1 −1 -1 0

A: The given matrix,The aim is to find the inverse of the matrix.

Q: Fill in each blank so that the resulting statement is true.

A: Given 1       1       -1 −2−3    -4        2  4 2         1       1   6

Q: Find a 2 x 2 matrix such that 3 -2 -2 = 61

A:

Q: Explain Equality of matrices. Give a suitable example.

A: Equality of matrices:Two matrices are equal if all three conditions given below are satisfied: ·…

Q: What is the multiplicative identity matrix?

A: According to the question, we have to define the multiplicative identity matrix. As the above…

Q: Define the matrix square root?

A:

Q: -3-9 9 adj -2 -7 1 1 -9 -10 1

A:

Q: Define Matrix Inverse?

A: The inverse of matrix A with order 2×2 can be obtained by elementary row operation on a new matrix…

Q: Define Matrix Notation.

A: