Homework Answers
![» A- [2] Let us apply elementary Row operation on A to Reduce it to a Row echelon Matrix. A R₂ = R₂-4R, TA- 2 7 0 2 1 - 27 Ri](http://img.homeworklib.com/questions/9712c480-5a2d-11eb-a54b-792fcf412dda.png?x-oss-process=image/resize,w_560)
2. Consider matrix A = 5 0 1 2 Find elementary matrices E1, E2 and E3...
2. Consider matrix A = 5 0 1 2 Find elementary matrices E1, E2 and E3 such that E3E2E1A=I.
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary...
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary matrices associated with e and e-1, e = R 2 R, the e: Add - 2 times the second row to the third row of 3 x 3 matrices.
1 3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary...
1
3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1
3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1
1. The matrices A and C are row equivalent. Find the elementary matrices such that C...
1. The matrices A and C are row equivalent. Find the elementary matrices such that C = E,E,E,A. 3 2 1 -4 -6 0 1 7 2 1 2 1 0 5 3 0 2 -2 5 9 6 -3 6 3 3 2 1 -4
1. Let A and B be two 4 by 4 matrices with (let A =-2 and...
1. Let A and B be two 4 by 4 matrices with (let A =-2 and det B-1-8. Find det(-2.1' B) 2. Assume that A is a 4 x 4 matrix and det (Adj(A))-8, find det(A) 3. Find the inverse the given matrice by way of elementary row operations
2 er Let I be an interval of R, and define the function f :I→ R by f(x) 1 +e2z or every z EZ. (a) Find the largest...
2 er Let I be an interval of R, and define the function f :I→ R by f(x) 1 +e2z or every z EZ. (a) Find the largest interval T where f is strictly increasing. (b) For this interval Z, determine the range f(T) (c) Let T- f(I). Show that the function f : I -» T is injective and surjective. (d) Determine the inverse function f-i : T → 1. (e) Verify that (fo f-1)()-y for every y E...
Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1...
Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1 4 5
Given -1 1 A= = 20 0 find elementary matrices E1, ..., Ex such that Ex---E,...
Given -1 1 A= = 20 0 find elementary matrices E1, ..., Ex such that Ex---E, E, A = 13.
Q5 Eigenmatrix 8 Points Let C12 M2 = 211 221 : Xij ER ER} 2 22...
Q5 Eigenmatrix 8 Points Let C12 M2 = 211 221 : Xij ER ER} 2 22 be the vector space of 2 x 2 real matrices with entrywise addition and scalar multiplication. Consider the subspace W = {X E M2 : X = XT} of M2 consisting of symmetric matrices. (a) (2pts) Find a basis of W. What is its dimension? 1 (b) (2pts) Let A= Show that if X EW then AXAT EW. (c) (4pts) Consider the linear transformation...
SVD a) Let A E RX be an invertible matrix and i ER" be a nonzero...
SVD a) Let A E RX be an invertible matrix and i ER" be a nonzero vector. Prove that ||A7|| 2 min ||- b) Let A € R2X2 and 1 = plot of|ly|| vse. 2,17|| = 1. Now let y = Až. Below is the (cos(O)" A has the SVDUEVT. Either specify what the matrices U, 2, and V are; or state they they cannot be determined from the information given. c) Let A E RNXN,B E RNXN be full...
2. Consider matrix A = 5 0 1 2 Find elementary matrices E1, E2 and E3 such that E3E2E1A=I.
4. For the given elementary row operation e, find its inverse operation e-1 and the elementary matrices associated with e and e-1, e = R 2 R, the e: Add - 2 times the second row to the third row of 3 x 3 matrices.
1
3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1
3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1
1. The matrices A and C are row equivalent. Find the elementary matrices such that C = E,E,E,A. 3 2 1 -4 -6 0 1 7 2 1 2 1 0 5 3 0 2 -2 5 9 6 -3 6 3 3 2 1 -4
1. Let A and B be two 4 by 4 matrices with (let A =-2 and det B-1-8. Find det(-2.1' B) 2. Assume that A is a 4 x 4 matrix and det (Adj(A))-8, find det(A) 3. Find the inverse the given matrice by way of elementary row operations
2 er Let I be an interval of R, and define the function f :I→ R by f(x) 1 +e2z or every z EZ. (a) Find the largest interval T where f is strictly increasing. (b) For this interval Z, determine the range f(T) (c) Let T- f(I). Show that the function f : I -» T is injective and surjective. (d) Determine the inverse function f-i : T → 1. (e) Verify that (fo f-1)()-y for every y E...
Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1 4 5
Given -1 1 A= = 20 0 find elementary matrices E1, ..., Ex such that Ex---E, E, A = 13.
Q5 Eigenmatrix 8 Points Let C12 M2 = 211 221 : Xij ER ER} 2 22 be the vector space of 2 x 2 real matrices with entrywise addition and scalar multiplication. Consider the subspace W = {X E M2 : X = XT} of M2 consisting of symmetric matrices. (a) (2pts) Find a basis of W. What is its dimension? 1 (b) (2pts) Let A= Show that if X EW then AXAT EW. (c) (4pts) Consider the linear transformation...
SVD a) Let A E RX be an invertible matrix and i ER" be a nonzero vector. Prove that ||A7|| 2 min ||- b) Let A € R2X2 and 1 = plot of|ly|| vse. 2,17|| = 1. Now let y = Až. Below is the (cos(O)" A has the SVDUEVT. Either specify what the matrices U, 2, and V are; or state they they cannot be determined from the information given. c) Let A E RNXN,B E RNXN be full...
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