4 (a) For the matrix B = find an orthogonal matrix P such that PT BP is a diagonal matrix. (b) Write down the sign property of p = 2x² + 2y² + 2z² – 2xy – 2yz - 2zx. As in 3(c), use an orthogonal transformation to express o in diagonal form. What does the equation p(x, y, z) = 0 mean?

Q: ] Given the following system of linear equations: Зх, + 4х, 1 2x, 2х, + X3 -1. 2.x, 2x, + 4x,…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Show that any two rows of a matrix can be interchanged by elementary row transformations of the…

A: According to the question,

Q: (ii,if i = j A =, if i +j if i # j ((i B = + 1)',if i = j j+1'if i # j

A:

Q: Find the matrix A of the rotation about the z-axis through an angle of pi/2, counterclockwise as…

A: To get the matrix A for a rotation about the z-axis through an angle of pi/2 counterclockwise, we…

Q: Let B=(b₁,b₂), C={C₁,C₂), be bases for R² b₁ = (-1,2), b₂ = (1, -1), C₁=(1,2), C₂ = (1,1) Find the…

A:

Q: Find the standard matrix of the linear transformations describes as Reflection around x-axis…

A: When we reflect a point about x- axis , x coordinate remains same , and sign of y-coordinate changes…

Q: Find the matrix of the linear transformation that sends a vector to its reflection to the plane x1 –…

A: To find : matrix of the linear transformation that sends a vector to its reflection to the plane…

Q: Tis a linear transformation from R² into R² as shown below. The standard matrix for T-l is T'x, у)…

A: According to the given information, Let T be a linear transformation from R2 into R2 as:

Q: Suppose T: R² R² is a linear transformation that first reflects points across the ₁-axis and then…

A:

Q: 3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that…

A: Trace of matrices is sum of its  diagonal entries

Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: 2)} and 0 4 A = 2 3 . be the matrix for T: R2 → R? relative to (a) Find the transition matrix P

A: Note: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: (a) find the standard matrix A for the linear transformation T, (b) use A to find the image of the…

A: We find the matrix A so that v , Av are 2x1 matrices.

Q: 10. Let *-{0] [8] []} B B is a basis of R³. Let T: R³ R³ be the linear transformation given by T(v)…

A:

Q: A B -2 -2

A:

Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: Express A as a product of elementary matrices where 3 A = [2²4] 1 And express each elementary matrix…

A: Let us find the elementary matrices.

Q: Use the standard matrix for the linear transformation to find T(v) T(x, y, 2) = (2x + y, 3y – 2), v…

A: Given : T(x, y, z) = 2x + y, 3y - z v = 0, 1, -1   To find T(v).

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: Find the standard matrix of the given linear transformation from R2 to R2 Projection onto the line y…

A:

Q: 2. Let a = 3 and 6 -4. (a) Graph the parallelogram spanned by a and b. Find if C' is matrix whose…

A:

Q: Find the 3x3 matrix that produces the described composite 2D transformation below, using homogeneous…

A: To Determine :- The 3 × 3 matrix that produces the described composite 2D transformation below,…

Q: Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix…

A: As per guidelines of bartleby we solve only first three parts.

Q: (1 point) The matrices - [8]. [J]. -[i]·.^ - [i]· A A4 = A₁ = A3 = A₂ = form a basis for the linear…

A:

Q: Given a line AB and the coordinate for A is (2,1) and B (2,3). AB will be rotated 900…

A: Given segment AB  (shown below).  Center of point of rotation C(1,1).…

Q: Let = 3 -] A = vectors in K is defined by al b1 a2b3-a3b2 EX6H a2 xb2 a3b1-a1b3 a3 La1b2-a2b1 Find…

A:

Q: Consider the matrix A = show that the product L(X)=Ai is a linear transformation, where žER*.

A:

Q: Q2: Determine the Transformation matrix that transfer the shown object to its final destination…

A: Given a circle at the starting point 6,-1 and the ending point 5,4.5. The translation matrix is…

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: Find the image of the point (x, y) under the matrix transformation that first reflects the point…

A: