Inverse matrices

In R, if we want to compute the inverse of a matrix we can use the inv() function from the matlib package. For example,
If we want to see the output in terms of rational numbers, then we can use the fractions() function from the MASS package
In R we can use the solve() function to find the inverse of a matrix instead of the inv() function. For example,
  1. True or False: Suppose A is an invertible matrix. Then (A−1)−1 = A.
  2. True or False: Suppose we have m×m invertible matrices A, B, C. Then A−1A (B + C) = (B + C) A A−1.
  3. True or False: Suppose we have m×m invertible matrices A, B, C. Then (A + A−1) (B + C) = (B + C) (A−1 + A).
  4. True or False: Suppose we have m×m invertible matrices A, B, C. Then (A · B · C)−1 = C−1B−1A−1.
  5. Suppose we have \( \displaystyle {\bf A} = \befin{bmatrix} 7 & 0 \\ -7 & 7 \end{bmatrix} . \) CoCompute the inverse of A if one exists.mpute the inverse of A if one exists.

 

  1. Anton, Howard (2005), Elementary Linear Algebra (Applications Version) (9th ed.), Wiley International
  2. Beezer, R.A., A First Course in Linear Algebra, 2017.
  3. Fitzpatrick, S., Linear Algebra: A second course, featuring proofs and Python. 2023.