[main] Added quiz solutions

Author: cthacker-udel

pythonProblems/matrixpractice/rowreduction.py

@@ -138,3 +138,94 @@
 # 7f + 5a + 3c = 120
 # 3f + 2a + 5c = 70
 # f + 2a + c = 20
+
+# [[3, 1], [1, 2]] # [[a, b], [c, d]] with the identity matrix [[1, 0], [0, 1]] (which returns the same matrix)
+
+# [[3, 1]] * [[a, c]]
+# [[3, 1]] * [[b, d]]
+# [[1, 2]] * [[a, c]]
+# [[1, 2]] * [[b, d]]
+
+
+# 3a + 1c = 1
+# 3b + 1d = 0
+# 1a + 2c = 0
+# 1b + 2d = 1
+
+
+# [[5, 2], [1, 2]] # [[a, b], [c, d]] with the identity matrix [[1, 0], [0, 1]]
+
+# [5, 2] * [a, c]
+# [5, 2] * [b, d]
+# [1, 2] * [a, c]
+# [1, 2] * [b, d]
+
+
+# 5a + 2c = 1 # a + 2/5c = 1/5
+
+# 5b + 2d = 0 # b + 2/5d = 0
+# 1a + 2c = 0
+# 1b + 2d = 1
+
+
+#   a + 2c = 0
+# - a + 2/5c = 1/5
+# ------------------
+#     10/5 - 2/5c = -1/5
+#     8/5c = -1/5
+
+
+# c = (-1/5) * (5/8)
+# c = -5/40
+
+# c = -1/8 ## found it
+
+# 5a + 2(-1/8) = 1
+# 5a + -2/8 = 1
+# 5a = 1 + 2/8
+# 5a = 10/8
+# 5a = 5/4
+# a = 5/4 * (1/5)
+# a = 5/20
+
+# a = 1/4 ## found it
+
+
+#   b + 2d =   1
+# - b + 2/5d = 0
+# ----------------
+
+#     10/5 - 2/5d = 1
+# --------------------
+#     8/5d = 1
+
+# d = 5/8 ## found it
+
+
+# 5b + 2(5/8) = 0
+# 5b + 10/8 = 0
+# 5b = -10/8
+# b = -10/8 * 1/5
+# b = -10/40
+# b = -1/4
+
+
+# [[1, 1], [2, 2]]  # [[a, b], [c, d]] ## [[1, 0], [0, 1]]
+
+
+# [1, 1] * [a, c] = 1
+# [1, 1] * [b, d] = 0
+# [2, 2] * [a, c] = 0
+# [2, 2] * [b, d] = 1
+
+
+# 1a + 1c = 1
+# 1b + 1d = 0
+# 2a + 2c = 0
+# 2b + 2d = 1
+
+
+#    a + c = 0
+# -  a + c = 1
+# -------------------------
+#     Impossible to solve