Ask Your question
Need a fast expert's response?Submit order
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Search & Filtering
following linear system is consistent:
x − 3y + 4 = 0, 3x − 2y = λ, y = 6 − 2x .
Otherwise, alter the last equation in the system so that the solution can be obtained
by applying the Rule.
x + y + z = π
− πx + πy + √2z = 0
π^2x + π^2y+ 2z = 0
n^2 entries, where n ∈ N , then it is a square matrix. Is it true or false? Justify your answer.
b) what would be the gradient of a line perpendicular to the straight line
2. State whether the following pairs of lines whose equations are given are parallel, perpendicular or neither.
a. 2x-y+4=0 and 6x-3y+7=0
b. 7x+3y-8=0 and 3x-7y+1=0
c. x+3y-2=0 and 3x-y+4=0
3. Find the equation of the straight lines
a) Passing through the point (3, -2) and parallel to the line 4x-y+6=0
b) Passing through the origin and parallel to the line 5x+3y-7=0
c) Passing through the point (-2,5) and perpendicular to the line 3x-2y+8=0
a) 2x + 3y = 6
b) 4y - 2x + 5 = 0
2. The following equations are in the general form Ax + Bx + C = 0. Express each of them in the form y = mx + b and state the gradient and y intercept of its graph
a) 3x - y + 2 = 0
b) 3x + 4y + 12 = 0
c) 2x + y - 3 = 0
3. The line PQ had an angle of inclination of 60 degrees. What is it gradient? ( answer in surd form)
4. What is the equation of the straight line having:
a) a gradient of 3 and a y intercept of -4
b) an angle of inclination of 135° and a y intercept of 5
What conditions on the vectors u, v, w ∈ R3, would create an object that is not a plane?
. T(x, y, x)=(x+y, y, 2x-2y+2z)
Check that T satisfies the polynomial (x-1)square(x-2). Find the minimal polynomial of T.
solution, (b) an infinite number of solutions, and (c) a unique solution.
ax1 + x2 + x3 = 1,
x1 + ax2 + x3 = 1,
x1 + x2 + ax3 = 1.
8x1 -x2 +2x3 =4
-3x1 +11x2 -x3 +3x4 =23
_x2 +10x3 -x4 =-13
_2x1 +x2 -x3 +8x4 =13
with x^(0) =[0 0 0 0]^T by using the Gauss Jacoboi and Gauss Seidel method. The exact solution of the system is x=[1 2 -1 1]^T. Perform the required number of iteration so that the same accuracy is obtained by birth the methods. What conclusions can you draw from the result obtained?