00:01
In this problem we are provided with three vectors v1, v2 and v3.
00:07
The vector v1 equals to 0, 3, 1, negative 1, vector v2 equals to 3, 0, 5, 1 and vector v3 equals to 2, negative 7, 1 and 3.
00:21
Here we are asked to express each vector as a linear combination lc of the other two vectors.
00:36
So let us begin by representing the first vector as a linear combination of the other two, that is v1 equals to a v2 plus bv3.
00:46
So now making use of this condition for the first component that is 0 ,3 and 2, we have to obtain the equation 3a plus 2b equals to 0 and making use of this for the second component we obtain negative 7b equals to 3 and this gives us the value of b as negative 3 over 7.
01:12
So now we substitute this value of b here so we obtain 3a equals to 2 times 3 over 7 which implies that the value of is 2 over 7.
01:25
So now that we have obtained the values of a and b, we can substitute these back.
01:31
We get v1 equals to 2 over 7 v2 minus 3 over 7 v3.
01:38
And therefore, this is the required answer for expressing the vector v1 as a linear combination of v2 and v3.
01:46
So next, we express the vector v2 as a linear combination of v1 and v3.
01:54
So making use of the first component we get 2b equals to 3 which implies that the value of b is 3 over 2.
02:03
Next we make use of the second component...