Find T(v) by using (a) the standard matrix and (b) the matrix relative to B and B′.T: R3→R3, T(x, y, z) = (x + y + z, 2z − x, 2y − z), v = (4, −5, 10), B = {(2, 0, 1), (0, 2, 1), (1, 2, 1)}, B′ = {(1, 1, 1), (1, 1, 0), (0, 1, 1)}

Q: help me with this plz

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the characteristic equation of the matrix: 4 C = 2 -2 2.

A: Characteristic equation of the matrix C is given by  det ( C - λI ) = 0

Q: Find the matrix of the quadratic form associated with the quadratic equation 3x2 − 16xy + 3y2 − 13 =…

A: The given quadratic equation is 3x2-16xy+3y2-13=0. We have to find a matrix.

Q: Perform the elementary row operation - R₁ → R₁ to matrix D to obtain matrix E. -1 0 0 01 2 -2 -2 1…

A: Given a matrix A=1-10002-21240101000215 To perform the row operation -13R4→R4 to obtain a matrix E

Q: Let A be the matrix Compute A50

A:

Q: and find matrix Y such that 4 + 2} - 48.

A:

Q: Construct a matrix that stretches vectors in the direction V₁ = 22-Ĵ by a factor of 4 and leaves…

A:

Q: Find a 3 by 3 matrix that scales the point (x,y,z) by 2 in the x direction and 4.5 in the direction,…

A:

Q: Express the quadratic form (c₁x₁ + C₂X₂ + ... + Сnn)² in the matrix notation TA, where A is…

A:

Q: Q5) ẩ.ẩ jolve the eẩqẩuatẩionj; 2x²y dy/ldx + 2xy' +1= 0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Get a base for the column space of the matrix shown in the image

A:

Q: Find a 2 by 2  matrix that scales the point (x,y) by 0.5 in the x direction and 3 in the y…

A:

Q: For matrix A below, make a change of variables that decouples the equation x'=Ax. Write the equation…

A: We have to find the equation x(t) = Py(t) that leads to the uncoupled system y'=Dy for matrix A.

Q: -4x – y – 6z = -39 -9x + 7y + 4z = 47 – 7x – 6y + z = -52

A:

Q: Let B = {b1, b2} and C {C1, C2} be R2. Produce the change-of-coordinate matrix from B to C and from…

A:

Q: 7x + 8y 2 = 46 x - 3y 8z = -53 -2の+y+z=

A: Given the system,   7x+8y-z=46  x-3y-8z=-53-2x+y+z=1 We have to find the x,y,z using Reduced Echelon…

Q: , and c

A: Given quadratic form is, Here, A is symmetric matrix as,

Q: [a b] [add] c A² − (a + d)A + (ad – bc)I = 0 Show that the matrix A = satisfies the equation

A:

Q: 2 3 4 Let vi = 1 V2 = -2 V3 = 5, and E u = V2 3 Determine if u is in Col E, the column space of E.…

A: We have to determine u is in Col.E, the column space of E.

Q: Find the SVD of the matrix: 1 2 34 A = 0 0 0 0

A:

Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

A:

Q: Perform the elementary row operation R2 → R3 to matrix B to obtain matrix C. -1 0 0 01 1 2 4 2 -2 A…

A: Our Aim is to perform the elementary row operations R2↔R3 to the matrix given below:-

Q: Write down the 4×4 3D matrix to move by(xm,ym,zm).

A: A 4 by 4 Matrix 3D matrix used for the purpose of representing the given vectors is called…

Q: Find the 3x3 matrix that induces the described action on R3. Rotates the yz plane  by 45 degrees,…

A: We have to find 3×3 matrix that rotates the yz plane by 45 degrees and reflects the x-axis.

Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

A:

Q: Suppose V₁, V₂ € R³ are nonzero column vectors and V3 = 2v₁ - 32. What is the determinant of the…

A: Given: Suppose  are nonzero column vectors and  We have to find what is the determinant of the…

Q: -2 Find C, where matrix C = [3/2 -1/2

A:

Q: Given 2. A and B = ( 4 Find the matrix represented by: (iii) 3(A – 4B) (iv) B+ 3AT

A: The given matrices are A=254-2  and B=-1724. (iii) Evaluate 3(A-4B) as follows.…

Q: Find the symmetric matrix that corresponds to the quadratic form q(x, y, z) = 3x² + 4æy – y² + 8xz

A:

Q: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

A: We have to find all real numbers  for which the matrix  is diagonalizable in

Q: How would I write the following 2 functions in matrix notation? Q(h) = (h, 2h, 3h) F(x, y, z) =…

A: We have to write the function as matrix notation. The given function is Q(h) = (h, 2h, 3h) Clearly,…

Q: Q3:-a) Find the values of (x, y) for the following matrix equation: 3 [х — 2у 0ј 6. -2 -2 x+ y]

A: Given that we need to find the values of x and y for which the following matrix equation satisfied.…

Q: Write the 2X2 matrix associated to a reflection about the x axis.

A: