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Find the inverse to the matrix B whose rows are first (2 4); second (1 3).

Solution:

Here are the rows of the matrices starting with B and with I at each stage of the computation,

Start = stage 0
row 1 of B: (2, 4) row 1 of I (1, 0)
row 2 of B (1, 3) row 2 of I (0, 1)

Step 1: divide row 1 by 2
row 1 of B: (1, 2) row 1 of I (1/2, 0)
row 2 of B (1, 3) row 2 of I (0, 1)

Step 2: subtract row 1 from row 2 and replace row 2 by the result
row 1 of B: (1, 2) row 1 of I (1/2, 0)
row 2 of B (0, 1) row 2 of I (-1/2, 1)

Step 3: subtract twice row 2 from row 1 and replace row 1 by the result
row 1 of B: (1, 0) row 1 of I (3/2, -2)
row 2 of B (0, 1) row 2 of I (-1/2, 1)