Please help - I don't know how to start this question .
an unknown matrix A has 5 original row vectors v1,v2,v3,v4,v5. The following row operations are then performed on A in given order.
1. Row2 +3xRow1 = row 2
2. -2 x row4 = row4
3. row 2 + row 4 = row 2
4. row 5 - row 2 = row 5
after these row operations the new matrix has a row of zeros in the 5th row. write the 5th row v5 of the origional matrix A as a linear combination of the other original row vectors of A.
I think i should take v1 = 1 0 0 0 0, v2 =0 1 0 0 0 ect but I'm really stuck.
an unknown matrix A has 5 original row vectors v1,v2,v3,v4,v5. The following row operations are then performed on A in given order.
1. Row2 +3xRow1 = row 2
2. -2 x row4 = row4
3. row 2 + row 4 = row 2
4. row 5 - row 2 = row 5
after these row operations the new matrix has a row of zeros in the 5th row. write the 5th row v5 of the origional matrix A as a linear combination of the other original row vectors of A.
I think i should take v1 = 1 0 0 0 0, v2 =0 1 0 0 0 ect but I'm really stuck.
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No, don't use numbers, just use symbols.
Start with the following rows:
v1
v2
v3
v4
v5.
Now let's go through it.
After step 1 you have this:
v1
v2 + 3v1
v3
v4
v5
After step 2 you have this
v1
v2 + 3v1
v3
-2v4
v5
After step 3 you have this
v1
(v2 + 3v1) + (-2v4)
v3
-2v4
v5
After step 4 you have this
v1
(v2 + 3v1) + (-2v4)
v3
-2v4
v5 - (v2 + 3v1) - (-2v4)
That last expression is equal to 0. Set the expression equal to 0 and rewrite the equation so v5 is on one side.
Start with the following rows:
v1
v2
v3
v4
v5.
Now let's go through it.
After step 1 you have this:
v1
v2 + 3v1
v3
v4
v5
After step 2 you have this
v1
v2 + 3v1
v3
-2v4
v5
After step 3 you have this
v1
(v2 + 3v1) + (-2v4)
v3
-2v4
v5
After step 4 you have this
v1
(v2 + 3v1) + (-2v4)
v3
-2v4
v5 - (v2 + 3v1) - (-2v4)
That last expression is equal to 0. Set the expression equal to 0 and rewrite the equation so v5 is on one side.