Mark the statement True or False Justify the answer The equa

Mark the statement True or False. Justify the answer.

The equation x = x2 u + x3 v, with x2 and x3 free (and neither u nor v a multiple of the other), describes a plane through the origin.

Solution

If a linear equation is of the form y=mx +c then m represents the slope of the line and c is the y-intercept,i.e. the ordinate(y co-ordinate) where the line cuts the y-axis.

        The equation x = x2 u + x3 v
In our equations in slope-intercept form, like y = mx + b, passing through the origin also means that the    y-intercept (and x-intercept) is 0.

       From our equation if we take it as y=mx+b form y-intercept is 0.

          so,

                    the plane through the origin.