9 -4 0 0 A4 5 2 0 0 0 1 2 and consider the vector space R4 with the inner product given by v, w)Aw. Let 0 0 -2 and let W span(Vi, V2, V3 ). In this problem, you will apply the Gram-Schmidt procedure to vi, v2, v3 to find an orthogonal basis (u, u2, u31 for W (with respect to the above inner product). b) Compute the following inner products. (v2, u1) - Then u2 =Y2__v2.ul) ui,...
4. Let 0 1/2 5 0o 0 1/25 0 0 01/25 a) Compute exp(tA (b) Use part(a) to solve the initial value problem y '-A-y, y(0)
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14. Match tables (a)-(d) with the contour diagrams (I-(IV) in Figure 8.57 -1 01 -1 01 -1 2 1 2 0 1 0 1 1 0 1 0 -1 01 -1 2 02 0 2 02 1 202 (Iv) 321 0 1 23
14. Match tables (a)-(d) with the contour diagrams (I-(IV) in Figure 8.57 -1 01 -1 01 -1 2 1 2 0 1 0 1 1 0 1 0 -1 01 -1 2 02 0...
ſi 4 01 Compute the inverse of the matrix A = 1 5 0 7 1 1
3 2 0 3. Compute the product 0 01-1 0 013 4. If the matrix A from the previous problem represents a linear transformation T, determine: (a.) Is the mapping onto (b.) Is the mapping one to one (c.) Is the mapping homomorphic (d.) Is the mapping isomorphic (e.) What is the range space? The rank? (f) What is the null space? The nullity? (g.) Does this transformation preserve magnitude? 5. (a.) What is AT, the transpose of the matrix...
23. Compute if x1=2, x2=5 and x3=0. 24. Compute ∑ i = 1 3 x i f i if x1=1, x2=3, x3=4 and f1=f2=2, f3=5. 25. Compute if x1=1, x2=3, x3=4 and f1=f2=2, f3=5.
Exercise 1. (a) Find the inverse of the matrix 0 0 1/2 A= 01/ 31 1/5 1 0 (b) Let N be a nxn matrix with N2 = 0. Show (I. - N)-1 = IA+N. (Hint: Use the definition of the inverse.)
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
can I have the answer for (a)? thank u!!
14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For...
Let {dn}n≥0 denote the number of integer solutions a1 +a2 +a3 +a4 = n where 0 ≤ ai ≤ 5 for each i = 1, 2, 3, 4. Write the ordinary generating function for {cn}n≥0. Please express the ordinary generating function as a rational function p(x) /q(x) where both p(x) and q(x) are polynomials in the variable x.