Tutors Answer Your Questions about Linear Algebra (FREE)
Question 94: How to know whether two lines are intersecting or not without drawing them on the graph, when we know their start and end points?
Suppose if AB is a line with A(2,1) and B(6,5) and CD is another line with C(3,4) and D(5,2). If we Draw these two lines on the 2D Graph then these two will intersect. But how could i know that these two lines are going to intersect or not without drawing the line on the 2D Plane?
I will be very thankful to you if u can solve my query and suggest me any other links regarding this. Thanks inadvance. Hoping the earliest reply.
Click here to see answer by ichudov(507)   |
Question 1690: For each of the ff. quadratic equations, (a) identify the conic section represented (b) write the given equation in the standard form (c) give the properties (d) find the x and y-intercepts and (e) sketch the graph.
1. 2x^2-2y^2+20y-75=0
2. 9x^2+4y^2-36x+8y+31=0
I need the answers now. Thanks!
Click here to see answer by khwang(438) |
Question 2887: I need your help on these three problems....................
(1).
-4 5
-5
The determinant of the matrix A is 1. Find the missing element of the matrix A
a.1
b.3
c.6
d.–24
(2). Find the determinant of the matrix C.
C=
4 0 –7
3 0 6
-5 2 3
a.45
b.24
c.-90
d.-21
(3). Use Cramer’s Rule to solve y.
x-4y=4
4x-y=1
a.-8/15
b. –1
c. 17/5
d. 0
Click here to see answer by xcentaur(357) |
Question 2893: I need your help please...........
1. If the matrices A and B are the same size and A+B=A, then:
a. Each element of B is 1.
b. Each element of B is 0.
c. A-B=A.
d. B=I, the identity matrix.
e. B and C
2. For the matrices C and D below, find the value of the missing element in D that makes the matrix product CD=[10].
C=[10 15 -2 5] D=[2 -3 5]...
Click here to see answer by khwang(438) |
Question 3606: A guy has 30 coins consisting of nickels dimes and quarters. He has 3 more dimes than nickels. The total of the coins is $3.55. find the number of quarters. (I have done problems like this before without any problems but this one is giving me a really hard time. It seems simple but i cant get the correct solution..???
Click here to see answer by AnlytcPhil(1806)  |
Question 3703: 1. Find bases for the following subspaces of F5:
W1 = {(a1, a2, a3, a4, a5) Î F5: a1 – a3 – a4 = 0} and
W2 = {(a1, a2, a3, a4, a5) Î F5: a2 = a3 = a4 and a1 + a5 = 0}.
What are the dimensions of W1 and W2?
2. The set of all upper triangular n x n matrices is a subspace W of
M n x n (F). Find a basis for W and determine its dimension.
Click here to see answer by longjonsilver(2297)  |
Question 3698: 1. Find bases for the following subspaces of F5:
W1 = {(a1, a2, a3, a4, a5) Î F5: a1 – a3 – a4 = 0} and
W2 = {(a1, a2, a3, a4, a5) Î F5: a2 = a3 = a4 and a1 + a5 = 0}.
What are the dimensions of W1 and W2?
2. The set of all upper triangular n x n matrices is a subspace W of
M n x n (F). Find a basis for W and determine its dimension.
Click here to see answer by khwang(438) |
Question 4520: Let A be an m x n matrix. Prove that if B can be obtained from A by an elementary row (column) operation, then B transpose can be obtained from
A transpose by the corresponding elementary column (row) operation.
Click here to see answer by khwang(438) |
Question 4532: True or False:
a) The graph of f(x) = (x-3)^2 is the graph of f(x)=x^2 shifted a distance of 3 units to the right.
.
b) The equation (y^2/9) - (x^2/36) = 1 is a hyperbola that opens to the left and right.
.
c) (1/cubed root of x) = (1/cubed root of x) * (cubed root of x^2/cubed root of x^2) = (CUBED ROOT OF X^2/X).
.
D) The graph of f(x) = x^3 + 2 is the graph of f(x)=x^3 shifted upward a distance of 2 units.
.
e) The function f(x)=x^2 is not a one to one function.
.
f) The composition function of f o g and the product function of f * g are different. ( * is a colored in circle)
Click here to see answer by pushpaharan(47) |
Question 4563: Let T, U: V to W be linear transformations. Prove that:
a. R(T+U) is a subset of R(T)+R(U).
b. If W is finite-dimensional, then rank(T+U)=< rank(T)+rank(U).
c. Deduct from b that rank(A+B)=< rank(A)+rank(B) for any m x n matrices
A and B.
Click here to see answer by khwang(438) |
Question 4745: What facts concerning the solution of a quadratic equation can be
deduced from the discriminant of the quadratic formula? In other words,
what different types of solutions are possible depending on the
value of the discriminant? Please be specific about when these occur.
Click here to see answer by longjonsilver(2297) |
Question 4794: A quadratic equation always has two solutions. How do you account for
this difference when compared to linear equations? At what step in the
process do we ensure that we get two solutions when using the
Completing the Square method?
Click here to see answer by rapaljer(4671)  |
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