# Let B be a 4 times 4 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 colu

Let B be a $4×4$ 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 (so that the column dimension is reduced by 1).
(a) Write the result as a product of eight matrices.
(b) Write it again as a product ABC (same B) of three matrices.
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

izboknil3
Step 1
Note: Here multiple questions posted, answer to the first three subparts are given. If there is a need for remaining too, kindly post it again with the remark.
Let B be a $4×4$ matrix,
Let, $B=\left[\begin{array}{cccc}{b}_{11}& {b}_{12}& {b}_{13}& {b}_{14}\\ {b}_{21}& {b}_{22}& {b}_{23}& {b}_{24}\\ {b}_{31}& {b}_{32}& {b}_{33}& {b}_{34}\\ {b}_{41}& {b}_{42}& {b}_{43}& {b}_{44}\end{array}\right]$
where, (${b}_{ij}$) represents the element at the position, i'th row, and j'th column.${R}_{i}$ represents i'th row and ${C}_{j}$ represents j'th column.
Step 2
1) Double column 1:
${C}_{1}\to 2{C}_{1}$
$B\sim \left[\begin{array}{cccc}2{b}_{11}& {b}_{12}& {b}_{13}& {b}_{14}\\ 2{b}_{21}& {b}_{22}& {b}_{23}& {b}_{24}\\ 2{b}_{31}& {b}_{32}& {b}_{33}& {b}_{34}\\ 2{b}_{41}& {b}_{42}& {b}_{43}& {b}_{44}\end{array}\right]$
2) Halve row 3:
${R}_{3}\to \frac{1}{2}{R}_{3}$

Step 3
3) Add row 3 to row 1:
${R}_{1}\to {R}_{1}+{R}_{3}$
Jeffrey Jordon