Write vector o = <-2,5> in linear combination form show your work. Thanks!
To write the vector o = <-2,5> in linear combination form, we need to express it as a combination of two vectors, let's call them vector a and vector b, each multiplied by a scalar coefficient.
Let's assume vector a = <a1, a2> and vector b = <b1, b2>. Then, the linear combination form of vector o can be written as:
o = x * a + y * b
where x and y are scalar coefficients.
Using the given values for vector o, we have:
<-2, 5> = x * <a1, a2> + y * <b1, b2>
To solve for x and y, we can equate the corresponding components of both sides of the equation:
-2 = x * a1 + y * b1 (1)
5 = x * a2 + y * b2 (2)
Now, we need to find suitable values for vector a = <a1, a2> and vector b = <b1, b2> such that equations (1) and (2) are satisfied.
Let's try considering vector a = <1, 0> and vector b = <0, 1>. Substituting these values into equations (1) and (2), we obtain:
-2 = x * 1 + y * 0
5 = x * 0 + y * 1
Simplifying, we have:
-2 = x
5 = y
Therefore, the linear combination form of the vector o = <-2, 5> is given by:
o = -2 * <1, 0> + 5 * <0, 1>
This can be further simplified as:
o = <-2, 0> + <0, 5>
Thus, the linear combination form of the vector o = <-2, 5> is:
o = <-2, 0> + <0, 5>