4 (1) Find a matrix A „such that (A - 41)-1 3 1 (2) Let A be 3x3 matrix with 4 = 4 Find : (a) det(( 3 A)?(2 A)-') (b) det( 2 A-' + 3 adj (A)) (3)Find the values of a that makes the system has (a) unique solution (b) No Solution. 3 A 7 (4)Find the rank of a matrix 17 0 1 2 (5)Suppose that I : R3 → R2 „such that 2 T (e.) =...
Find the eigenvalues of the given matrix. [-14 -6 36 16 1) A) -2.-4 B)-4 C)-2 D) -24 The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities 2) A5 - 24A4-189A3-486A2 2) A) 0 (multiplicity 2),-9 (multiplicity 2),-6 (multiplicity 1) B) 0 (multiplicity 1),9 (multiplicity 3), 6 (multiplicity ) C) 0 (multiplicity 2),9 (multiplicity 2),6 (multiplicity 1) D) 0 (multiplicity 2),-9 (multiplicity 2),6 (multiplicity 1) Diagonalize A- PDP-1 the matrix A, if...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
For a matrix A 3 5 (a) Find a nonsingular matrix Q let D-AQ be a diagonal matrix b)Find the inverse of A 氿ㄧ '11.ril. IfA+小1, find the maximal and minin al values of毗孵. 2 For a matrix A 3 5 (a) Find a nonsingular matrix Q let D-AQ be a diagonal matrix b)Find the inverse of A 氿ㄧ '11.ril. IfA+小1, find the maximal and minin al values of毗孵. 2
please finish all blanks in 1) 2) and 3) For each transformation below, find the value of T(U). 1) Let T be a linear transformation from R to M22(R). Let B= 2 5 6 Let C= [ ][ 2 :11; }(31 70 165 -116 273 Let M = 135 -223 -490 -811 be the matrix transformation of T from basis B to C -255 -600 -993 -422 2 Let v= 0 The value of T(U) 2) Let T be a...
These are linear algebra problems. 1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is invertible, and if so, use the adjoint method Enter as a matrix, exactly in fractional from if required, if not invertible enter "NA" A-1 la b -2a -2b -2c d e f d = -2,find Given that g hi g-3d h-3e -3f -2a -2b -2c d f g 3d h 3e...
Exercise 24. Let 2 1 A =-1 3 1 0 -2 2 3 SDS-1. (i) Find a nonsingular matrix S and a diagonal matrix D such that A (ii) Find a matrix B that satisfies B2 = A Exercise 24. Let 2 1 A =-1 3 1 0 -2 2 3 SDS-1. (i) Find a nonsingular matrix S and a diagonal matrix D such that A (ii) Find a matrix B that satisfies B2 = A
11 -2 31 Let A = 2 1 k Find the value of k for which det A = -10. Your value of k should be an integer 10 -3 -k] Answer: Check Let [ 2 2 -1] A = -1 -11 ( 2 4 -1] Given that 1 is an eigenvalue of A, find a value of k so that (5.-1,k) is in the eigenspace of A corresponding to the eigenvalue I.
Question 7 (Chapters 6-7) 2+2+2+3+2+4+4-19 mark Let 0メs c Rn and fix r' E S. For a R" consider the following optimization problem: (Pa) min ar res and define the set K(S,) (aER z" is a solution of (Pa)) (e) If z' e int(S), prove that K(S, (0) (1) If possible, find a set S CR" and s* E S such that K(S,) (g) Let SB, 0.1] (rR l2l3 1) (the closed (, unit ball) and consider (1,0)7. Prove that...
For each transformation below, find the closed form of the transformation. 1) Let T be a linear transformation from R$ to M22 (R) [i Let B=1 0:00 [. :] [11] [12] [0 ] Let C= 12 41 -17 -5 65 -27 92 Let M = be the matrix transformation of T from basis B to C 17 58 -15 -51 81 The closed form of the transformation is Tb 3-1 2) Let T be a linear transformation from P3(R) to...