3. Transform the DE: (12-7t+6)y" + 3y²+ 5ty = sec(t); y(4) =1, y'(4) = 3 into a system of two first order DE in matrix form. Give the interval of t for FEUT to apply.

(11) Let -9 ·(?), a=(-4). b₁ = b₂ = - i), 2-(-³). (₁ = Let B = {b₁,b₂} and let C = {C₁, C₂} be bases for R². Find the change of coordinates matrix P from B to C.

A=30 ,B=20, C = |,D= 22 Find the 3x3 homogeneous matrix for 2D-reflection across a line that goes through (B, C) and makes an angle at +D degrees (counterclockwise) from the x-axis.

a) For invertible matrices A, BE RXn, show that ((AB)")- = (A-1)T (B')". %3D b) Let A, B, C, DE RX" be invertible matrices and suppose A" = c" (A-' D)") B. Solve for D in terms of A, B, C, their transposes, and their inverses. Your answer should not contain any nested expressions in parentheses. + Drag and drop an image or PDF file or click to browse...

Help with the following question

Give a matrix representation of the quadratic form f(x, y, z) = 4x 2 + 9y2+ 16z 2 − 2xy + 4xz − 6yz  and determine if the quadratic form is positive or negative definite.

Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R² R², T(x, y) = (2y, 0), v = (-8, 4), B = {(2, 1), (-1,0)), B' = {(-1,0), (2, 2)) (a) standard matrix T(v) = (b) the matrix relative to B and B' T(v) =

Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let 3 2 40 be the matrix for T: R2 R2 relative to B. 56°F A = (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [v] and [T(v)]B, where [v]B = [-5 4]T. [V] B [T(v)]B = (c) Find P-1 and A' (the matrix for T relative to B'). p-1 = 4

Write the system of equations in the image in matrix form

Let B = {(1,3), (-2,-2)} and B' = {(-12,0), (-4,4)} be bases for R2, and let  A= 4 3 0 2 be the matrix for T: R2 -> R2 relative to B