Show that there do not exist scalar c1 c2 and c3 c1(-2,9,6)+c2(-3,2,1)+c3(1,7,5)= (0,5,4)​

This is the same as showing the following system of equations doesn't have a solution:

or in matrix form,

The quickest way to check if there is a solution is to check whether the coefficient matrix is invertible. If its determinant is 0, then it is not invertible.

And the quickest way to show that the determinant is 0 is by observing that the third row is a linear combination of the first two rows:

(-2, 9, 6) - (-3, 2, 1) = (-2 + 3, 9 - 2, 6 - 1) = (1, 7, 5)

So there are indeed no such scalars c₁, c₂, and c₃.

g

step-by-step explanation:

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct