2. factor 1/4, then reflects about the line y = x. = (1/4 ( (a) A Find the standard matrix for the operator on R² which contracts w (d) A = 1 1/4 0 ) 0 1/4 1/4 0 0 - (1¹/4) 0 (e) None of these (b) A = (c) A = (!)

Q: if matrix A is ] and matrix B is will have same result matrix. • (AB)T # B'AT 1 Add file if matrix A…

A:

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

A:

Q: [a11(t) a12(t) 1) Let A(T) = be differentiable. %3D Show that: d (det (A(t)) = det a 12 (t)] la21(t)…

A:

Q: 6. O True/false. Give a one sentence justification. A singular 2 x 2 matrix can have determinant 1;…

A:

Q: Identify the matrix that represents each linear transformation below. Write A, B, C, D, D or F. ^ -…

A:

Q: Find the determinant of the following matrix (CLO7) ^= [41] Select one: O a. -3 O b. 5 C. -7 O d. 7

A: Given: Matrix:A=[2,5−1,1​​] Calculate the determinant for the matrix. Let`s assume a value for each…

Q: 21.1f A' = 34² where A is n by n matrix, then (a) A= 31 (b) A 31 if rank((A) =n () A" =!1 (d) a and…

A:

Q: Find f(B)

A:

Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

A: This problem is related to the vector algebra. The problem is solved in the following image.

Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

A:

Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

A:

Q: For matrix A and a scalar k, (kA)T is equal to: k(A^T) k(A) (k^2) x (A) (k^2) x (A^T)

A: We will solve the matrix operation.

Q: How is the matrix of R^−1 obtained from that of R in general, that is, when A = {a1, . . . , am}, B…

A:

Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

A:

Q: Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

A: To find: dimcol(A)⊥ Given information: A is 8×4 matrix such that rank(A)=3. Concept used:…

Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: (31/1/2 03 A= 1 1 - 1 3 3 3 1 0 0 0 0 0 0 0 -130 0 0 10 3/

A: According to the given matrix A, find an invertible matrix P such that .

Q: y = [ 0 1] (2x2 matrix) + [-1 0] d/dx y [1] (1x2 matrix) y (0) [1] [1] %3D [2]

A:

Q: t A be the square matrix (abcd) A. If ad−bc = 1, then show that A^−1 =(d−b−ca ) B. If ad−bc=α, then…

A: If  is a square matrix then its inverse is where

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: Let T: R³ R² be defined by T → Let B3 = 6 ----A-D-A---M--N} and C 5 {" (6) - L U₂ -3x1 3x2 + x3 7 {…

A:

Q: 3. Find all matrices which satisfy the matrix equation (::)(; })-(; :)(::)

A: Here,

Q: 8 Consider a square matrix B whose inverse is given by B'. a In terms of B", what is the inverse of…

A:

Q: 16 21 Let A = |-14 -19 Find two different diagonal matrices D and the corresponding matrix S such…

A: Given matrix is A=1621-14-19 We find the eigenvectors. For eigenvalues, A-λI=0⇒1621-14-19-λ…

Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: A and B are n x n matrices.    check the true statements below:   1) det(A)det(B) = -det(B^(t)A^(t))…

A: The objective of the question is to verify the truthfulness of two statements related to the…

Q: Write f= x + 10x1x2 + x3 as a difference of squares, and f= x? + 10x,x2 + 30x as a sum of squares.…

A: Given f=x12+10x1x2+x22.  Let the associated matrix of f be A=abba is 2×2 symmetric matrix. Then,…

Q: 1. True or False: (Matrix [mxn]) [3x6][5x3]=[5x6] O True O False O Maybe

A:

Q: (a) Show that the jth column of the matrix product AB is equal to the matrix product Ab;, where b;…

A:

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: 10. (a) Show that the matrix is positive definite. (b) Find the square root of A, (A). (c) Write the…

A: In this question, the concept of the matrix is applied. Matrix A matrix is a rectangular array or…

Q: Let T: R³ → R² be defined by T -~--~--E) ----B]}~~(~-| ||-~ ~[]) Let B = u₁ U3 = { = [3], , = 6 (ED)…

A:

Q: Use determinant to find the equation of the line that passes through the points (4, ― 3) & ( ―1,2)

A: We have to find equation of line using given information Concept required: Equation of line passing…

Q: Express the quadratic equation in the matrix form x Ax + Kx + f = 0, where a Ax is the associated…

A: The given quadratic expression is .We need to convert this quadratic in the form .

Q: (2) Let A be 3x3 matrix with 4|| = 4 Find : (a) det(( 3 4 )²(2 4)') ) det( 2 A + 3 adj ( A ))

A:

Q: then the standard matrix of T is A = 20 17 38 -17 20 T ([²]) = [²9] 17 38 d T ([^]) = [³7], -3 -17…

A: Given: To Find: To determine the standard matrix of transformation T.