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- If you know that Ax = b where A is a matrix and x and b are
vectors, can you say for sure that x = A-1b? Why or why not?
- If A-1 exists, what is
(AA-1)(A-1A)T?
- Use elementary row operations on augmented matrices to solve these
systems of equations for x. Use Gauss-Jordan elimination for (a) and (c).
Use Gaussian elimination and back-substitution for (b) and (d).
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3x1 + 5x2 = 2 and
2x1 + 4x2 = 1
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2x1 + 9x2 = -3 and
x1 + 3x2 = 6
- Ax = b where
and
- Ax = b where
and
- Find the inverses of these matrices:
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- Use your solutions to problem 4 and the letter to number translation
that sets A = 1, B = 2, etc. to decode these messages.
- 126 60 148 65 using
- 90 45 260 145 using
- 1 18 40 73 53 96 using
- Choose a matrix that has an inverse and encode your own message. Use
the letter to number translation that sets A = 1, B = 2, etc. and tell which matrix you
used to encode your message.
- Use your solutions to problem 4 to solve these systems for x if Ax = b.
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- What is
(A-1)-1? Hint: Think about the definition of the
inverse of a matrix.
- What is the inverse of the matrix
if a, b,c ≠ 0?
- Make a general statement about the inverse of a diagonal matrix.
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