X = { Ø₁ A₁ A², 3 and X₂ = { 0, B, B², √ ² are o fields but X, U X₂ is not. Why?

Q: 2. Find the determinant and invers a) -3 7 9 1 3 4 b) 1 9 3.

Q: |1 2 3 0 1 1 1 (g) 0 0 1 3 100 2

Q: 6. Find UV (dot a) Ū · V = (2, 3, -

Q: 1. If x=27-3k and y = i +5j -4k, express each of the following in terms of i, j, k b) 2(3x+y)-3(4y…

Q: Every combination of v = ( 1 , -2, 1 ) and w = ( 0, 1 , -1 has components that add  to __ . Find c…

Q: 2. Prove that if AB = AC, then B need not equal C unless A is invertible.

Q: Find x, y, z and w if (::)-(; )-(.. ") 4 x + y 3 -1 2w z + w 3

Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

Q: 10.

Q: [10 0 A = |4 1 0 1 0 1 2 4 0 1 3 0 1 Determine whether or not A is invertible. (Justify your answer)

Q: 9) /(x) = 3 · -8 -6 -4 -2 | x + 1 20 18 14 1 12 10 8 ଣ 4 + 2 2 4 6 X

Q: Verify that (AB)T = BTAT.

Q: 6. Show that there is a one-to-one correspondence between the Cartesian products A x B x C and A x…

Q: 1. Lat A - [; : - and B = 2 2 1 3 4 (a) Compute AB. (b) Compute BA.

Q: 1 a 0 b 1 -1) 31 For which values of a and b is-2 invertible? Why?

Q: 7. Evaluate the determinate |1 2 (d) 2 5 2 5 7 1 5 8 (e) 1 7 9 5 5 12 3 2 1 (f) 2 3 4 1 4 1