# Let B be a 4x4 matrix to which we apply the following operations: 1. double column 1, 2. halve row 3, 3. add row 3 to row 1, 4. interchange columns 1

Let B be a 4x4 matrix to which we apply the following operations:
1. double column 1,
2. halve row 3,
3. add row 3 to row 1,
4. interchange columns 1 and 4,
5. subtract row 2 from each of the other rows,
6. replace column 4 by column 3,
7. delete column 1 (column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product of ABC (same B) of three matrices.
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crocolylec

(a) To write the result as a product of 8 matrices.
Perform the following operations to get the final answer.
1.(BP)
2.Q(BP)
4.R(Q(BP))
5.R(Q(BP))S
6.T(R(Q(BP))S)
7.T(R(Q(BP))S)U
8.T(R(Q(BP))S)UV

(b) To write the result as a product of 3 matrices.
Multiply the matrices TRQ and name it as A. Multiply the matrices PSUV and name it as C. The representation ABC is the required product.