Task 1 For sub-tasks 1st, 2nd, 3rd, 4th, decide which statements are correct and which are not. It is not necessary to justify your answers. {Q can 1write a little bit) 1) Here we look at linear images v ) A - v for a 2 x 2- matrix A and vectors v=(v1,v2]"TER"2 (a) (b) (C) (d) 112 . 1"!) A.\" a) (v) is an eigenvector of A. The associated eigenvalue is approximately (0.5). b} (v) is an eigenvector of A. The associated eigenvalue is approximately (2}. c) (v) is an eigenvector of A. The associated eigenvalue is zero. d} (v) is an eigenvector of A. The associated eigenvalue is approximately (two) 2) Letm\" (mm) and v6 R I" n for I15\"; n21 an eigenvectorforA to the eigenvalue A. (a) It is necessarily true that (A A - I) = O. (b) It is necessarily true that (7t. - A - I) = 0. (c) It is necessarily true that it (A) = 0. (d) It necessarily holds that it (A) = A 3) Below are illustrations (level curves) and algebraic expressions of functions depending on two real variables (x and v). The task is to assign the images to the formulas. H H rmm=% (1&3!!!) = 32 _y u (a) The assignments are (i) (>f, (ii) (>g, (iii) (>h, (iv) (>k. (b) The assignments are (i) g, (ii) h, (iii) (>f, (iv) k. (c) The assignments are (i) ()k, (ii) ()h, (iii) ()g, (iv) (>f. (cl) The assignments are (U (>h, (ii) ()f, (iii) ()g, (iv) (>k . Maw=yhh \" \"3.3 2 May) = sin(m) - cos(2 - y). 4) Below is the direction field of scalar differential equations y ' (x) = f (x, y (x)). (a) (b) Her har vi f(x, y) = 1-y. Her har vi f(x, y) = x- y. (c) (d) Differensislligninga er autonom. Alle likevektslosningene til differensislligninga er stabile. - a) Here we have f (x, y) = 1 - y. b) Here we have f (x, y) = x - y. c) Differential equations autonomous. d) All equilibrium solutions to the differential equation are stable