Question

1 = 1 -3 k -1 -3 Let A=; and B -2 -2 0 2 k? 3 0 0 a. which matrix Cis defined? Explain why. i) ii) C = 2 BTA C =-2 B'AT C =- ATB b. calculate the product from task a. when the matrix C is defined. c. calculate the B. d. show and explain for which k-values should the equationssystem B==> have only solution == |

I would really appericate help, the task is in the picture/screenshot.

Let     A =  *see picture and   B = *see picture*

a. which matrix C is defined? Explain why.

b. calculate the product from task a. when the matrix C is defined.

c. calculate the B.

d. show and explain for which k-values should the equationssystem Bx=0 have only solution x=0.

Answer 1

c. we can not find B , because we dont have other information.
A- 1 B 1 1 - 1 / 2 K 2 2x3 3 O 3x3 2 BA of order 343 A 2%3 [ ] 3x3 . [ ] 2 x3 = not defined these must be equal. ii) = -28T AT -2. [37] [AT] axa 3x3 =) defined same 101 c = -ATB [AT] * [B] 373 3x2 =) not defined not equal c=-2 BT AT k 3 -2 6 2 - 2 - 2 3 3 O K .(-) to. (-3) + 3. 1 k. (-2) to. (-2) +3. (4) t.1).(-1) + 2 .(-3) +0.) (-1. (-2) + 2 (-2) + 0.1 -3. (1) + x² (-3) to. I + 3).(-2) + K?(-2) totul

t +3 -2k 2 3 2 2 3- 3k² 6-26² ak-6 4K + 3 C = 10 6k ? 2,6 ut ²-12 Aus.

one solution is (p=0) =) Homogenous determinat of B & 0 k ㅓ B) = 70 o 2 ka 3 o = K(2.0-0.k?) + 1 (0.0-3.k²) -3 (0.or? - +18 3K² +0 3k2 k to 7 18 thay Ax=0 other then must or k= -56 have sol nco