D Question 1 Question 1 Let A (5,-2, 6), B (5.-9,3), C (3.-4. 1) be three...
Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-equivalent to A, where 1 0 1 0 1 0 1 -2 0 5 0 0 01 3 (a) Find: the rank of A the dimension of the nullspace of A (b) Find a basis for the nullspace of A. Enter each vector in the form [x1, x2, ...]; and enter your...
Question 5 True of False part II: 5 problems, 2 points each. (6). Let w be the x-y plain of R3, then wlis any line that is orthogonal to w. (Select) (7). Let A be a 3 x 3 non-invertible matrix. If Ahas eigenvalues 1 and 2, then A is diagonalizable. Sele (8). If an x n matrix A is diagonalizable, then n eigenvectors of A form a basis of " [Select] (9). Letzbean x 1 vector. Then all matrices...
vector a= -2,5,-2 b= 2,2,5 Question 2 Question 2 Calculate the scalar and vector projection of bonto a (leave your answers in fractional form). Please note: Vectors a and b were calculated in Question 1 Formulae: a.b Compab= "scalar projection" lal Projąb = (Compoba = Thea -)a "vector projection" a → unit vector a
Let A = 10-o] 0 2 -3 and b = - 4 4 3 . Denote the columns of A by a, a, az, and let W = Span{a.a.az). a. Is b in aa.az)? How many vectors are in a .a .a? b. Is bin W? How many vectors are in W? c. Show that a is in W. (Hint: Row operations are unnecessary.] a. Is b in {a .az.az)? No Yes O How many vectors are in aaa? A....
Use octave to code and use disp to print entire vectors of numbers. 6. Consider two column vectors b azand b= [ 23 ] The dot product between a and b is given by the scalar d=a.b=a+b = 4,61 + a2b2 + a3b3. The dot product also satisfies the relationship a. b = |||||||| cos(0) where al = a.a is the length of a and is the angle between a and b. The cross product between a and b is...
Part c and d Question 5 (30 marks) Let A1, B(3,-5,0) and C(-1,4,1) be three points in R. Use vector method(s) to solve each of the following. R-8 (a) Find the unit vector u in the direction of AB-3AC. (b) Calculate the smaller angle betwen AB and AC. Correct the answer to ONE decimal place. (c) Find the shortest distance between B and the line passing through A and C. Correct the answer to ONE decimal place. (Hint: Consider the...
Question 4 options: A. i=1,2,5 only B. i=1,2,6 only C. i=5,6 only D. i=1,2,3,4 only E. i=4,5,6 only Question 5 options: i=1,4 only i=1,2,3,4,5 only i=1,2,4 only i=3,4,5 only i=1,2,5 only Consider A1 = 1 2 3 2 3 4 1 5 8 A2 1 2 3 5 6 7 3 4 5 3 4 5 = A3 1 2 3 4 4 3 2 1 6 6 6 6 = 1 1 1.- G?).-)-(13) ) 9 2 Let x=...
-4 6 6 5 0 Let A -17 4 4 B 1 3 1 -6 0 -6 0 0 DC- 8 0 0 8 0 1 10 0 0 4 AB BC Prove WITHOUT using the product property of determinants: If M, N are upper triangular matrices, |MN| = |M|N|. This question will be graded after the due date.
1 point) -3 Let A-3 4 14 and b- 12 -12 1 1 -4 -57 -24 Select Answer1. Determine if b is a linear combination of Ai, A2 and A3, the columns of the matrix A. If it is a linear combination, determine a non-trivial linear relation. (A non-trivial relation is three numbers that are not all three zero.) Otherwise, enter O's for the coefficients Ai+ A2t A, b. 1 point) Determine if the given subset of R3 is a...
Full answers and working out please. B -B (A+B) (B+A) (A-B) B FIGURE 1.3 FIGURE 1.4 (1) Addition of two vectors. Place the tail of B at the head of A; the sum, A+B, is the vector from the tail of A to the head of B (Fig. 1.3). (This rule generalizes the obvious procedure for combining two displacements. Addition is commutative: A+B=B+A; 3 miles east followed by 4 miles north gets you to the same place as 4 miles...