please solve question 4 Problem 7 Prove or disprove the following statements:(1) Let T: R3 → M2x2 be a linear map that is injective. Then T is also surjective.(2) A is an n x n matrix, such that 2A3 – 4A? + 6A – 21 = 0 (where I is the identity matrix andO is the zero matrix) then A is non singular.(3) If A and B are 3 x 3 matrices such that det(A) = 5 and det(B) = 4,Then det(A" (5B)-1) =1003 0 01 4 05 0 440 00 3 00 4(4) Consider the following 2 matrices: A =and B =Then A is similar to B.

Answered: Image /qna-images/answer/622c9fa9-5bf7-4135-805a-84dab16c49c3.jpg

Answered: ()- 40 0 0 3 0 0 0 4 300 1 4 0 5 0 4…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8AEXP

See similar textbooks

Similar questions

1. Use matrix inversion to solve for x, y, and z if:x + 2y + 2z = −1y − x − z = 02z + 3y + 3x = 1
1) Verify whether the limit to infinity of n(n + 1)(n + 2)−1(n + 3)−1 is equal to one. 2) Given matrix A (2/3 | -1/5) =, and that h(T) = T2 − 2T − 7, find h(T).
(2.5) Prove that if X, Y and X + Y are invertible matrices of the same size, thenX(X¹+Y-¹) Y(X+Y)-¹ = 1.
Consider the following optimization problem maximise Z = −3|x1| + x2 subject to 2x1+x2≥2 x1 − 2x2 ≥ −10 x1∈R, x2≥0. (a) Is this problem an LP problem in its current form? Explain your answer. (b) Convert this problem to an (equivalent) LP problem of the following form: Maximise Z = c⊤x subject to Ax = b with x≥0, x∈Rn where c∈R^n, 0 ≤ b ∈ R^m and A is an m×n matrix, for some n and m. Explain every step you make. In particular, define every variable that you introduce and explain why it is needed.
(4) Given matrix A = ( 2 −1 3 5 ) , and that h(T) = T 2 − 2T − 7, find h(T). ??????? ??? ? (1) A course repeater claims that his brother who did some Calculus at college years ago, but currently on some cough medication, believes that the first derivative of f(x) = (2x 2 − 1)(x 2 + 3) x 2 + 1 is f ′ (x) = [ 4x 2x 2 − 1 + 2x x 2 + 3 − 2x x 2 + 1 ][ (2x 2 − 1)(x 2 + 3) x 2 + 1 ] and that the first derivative of g(x) = (x 2 + 8) 7 (2 − 3x2) 5 is g ′ (x) = [ 14x x 2 + 8 + 30x 2 − 3x2 ] [ (x 2 + 8) 7 (2 − 3x2) 5 ] Using the product, qoutient and chain rules you learnt in Unit 7 of this Course, could you confirm whether his brother is right, wrong or a little tipsy. (2) In the following triangle below, the degree measures of the three interior angles and two of the exterior angles are represented with variables and expressions. (a) Find the size of each of the interior angle.
Under what condition is the function harmonic? Here A = (aij ) is a given, symmetric 3 × 3 matrix.
In this problem, allow T1: ℝ2→ℝ2 and T2: ℝ2→ℝ2 be linear transformations. Find Ker(T1), Ker(T2), Ker(T3) of the respective matrices:
Here you have to show that for the given A and B matrix in the question (AB)-1 = B-1 A-1

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

()- 40 0 0 3 0 0 0 4 300 1 4 0 5 0 4 (4) Consider the following 2 matrices: A = and B Then A is similar to B.