Find the value(s) of h for which the vectors are linearly dependent. Justify your answer. [Start 3 By 1 Matrix 1st Row 1st Colu
mn 3 2nd Row 1st Column negative 3 3rd Row 1st Column 6 EndMatrix ], [Start 3 By 1 Matrix 1st Row 1st Column 6 2nd Row 1st Column negative 9 3rd Row 1st Column 11 EndMatrix ], [Start 3 By 1 Matrix 1st Row 1st Column negative 2 2nd Row 1st Column 2 3rd Row 1st Column h EndMatrix ]The value(s) of h which makes the vectors linearly dependent is(are) nothing because this will cause ▼ x 1 x 2 x 3 to be a ▼ basic free variable. (Use a comma to separate answers as needed.)
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The Equation of a Line
The slope-intercept form of a line can be written as:
y = mx + b
Where m is the slope of the graph of the line and b is the y-intercept.
In the specific case where the line passes through the origin (0,0), we can find the value of b by substituting x=0 and y=0:
0 = m(0) + b
Solving for b:
b = 0.
Thus, the equation of the line reduces to:
y = mx
We only need to find the value of the slope.
That is where we need the second data. Our line is perpendicular to the line of equation 4x + 3y = 6.
Solving for y:
The slope of the second line is -4/3.
We must recall that if two lines of slopes m1 and m2 are perpendicular, then:
Substituting the value of m1 and solving for m2:
The slope of our line is 3/4 and the required equation is:
From this last equation, we need to find the general form of the line.
Multiply both sides of the equation by 4:
4y = 3x
Subtract 3x on both sides:
4y - 3x = 0
Reorder:
-3x + 4y = 0