Question

determine bases for the following subspaces of R^3 a) the plane 3x-2y+5z

Answer 1

Thank you, luck :^)

Answer 2

sir its my pleasure that you are helping me

Answer 3

That plane 3x - 2y + 5x = 0 is a two dimensional subapace of
\[\mathbb{R}^{3} .\]
If we solve for z in terms of x and y, we get
z = (-3x + 2y)/5. Letting x = 1, y = 0
makes z = -3/5.
Letting x = 0, y = 1 makes z = 2/5, so two linearly independent vectors in the subspace are
[1,0,-3/5] and [0,1, 2/5]. Those two vectors form a basis for the subspace \[B = \left\{ [x, y, z]|3x - 2y + 5z = 0 \right\}.\]

Answer 4

Consider the operation on p2 that takes ax^2+bx+c to cx^2+bx+a . Does it correspond to a linear transformation from R^3 to R^3 ? If so, what is its matrix? (b) Consider the operation on p3 that takesax^3+bx^2+cx+d to cx^3-bx^2-ax+d . Does it correspond to a linear transformation from R^3 to R^3 ? If so, what is its matrix?

Answer 5

can you solve above question

Answer 6

Someone help on my problems.

Answer 7

Let us consider n, a unit normal vector to the plane at the origin, and
\[u_1 ,\]
the unit vector in the direction of [1, 0 ,-3/5].
\[n = [3, -2, 5]/\sqrt{3^{2} + (-2)^{2} + 5^{2},}\]
\[u_1 = [5/\sqrt{34}, 0 -3/\sqrt{34}].\]
If we take the cross product of unit normal vector N with \[u_1 ,\]we get another unit vector \[u_2\]in the subspace S, so those two vectors form another basis if S; in fact, it is an orthonormal basis of S. To determine what \[u_2\]is, evaluate the determinant of matrix
[[ i, j, k ],
[3/sqrt(38), -2/sqrt(38), 5/sqrt(38)],
[5/sqrt(34), 0, -3/sqrt(34)]]

= [6/sqrt(1292), 34/sqrt(1292), 10/sqrt(1292)], simplifying to
[3/ sqrt(323), 17/sqrt(323), 5/sqrt(323)
]. Thus, an orthonormal basis for subspace S is\[\left\{ u_1, u_2 \right\},\]where \[u_1 = [5/\sqrt{34}, 0, -3/\sqrt{34}],\] \[u_2 = [3/\sqrt{323}, 17/\sqrt{323}, 5/\sqrt{323}].\]

Answer 8

solve this please
(b) Consider the operation on p3 that takes ax^3+bx^2+cx+d to cx^3-bx^2-ax+d . Does it correspond to a linear transformation from R^3 to R^3 ? If so, what is its matrix?

Answer 9

luck you should be asking one question at a time as a new one so he can get more medals for such awesome answers ;D

Answer 10

Thank you, luck :^)

Answer 11

sir can you solve the question i posted recently

Answer 12

Let me see can I find it...