PICTURE 1 : - A, B
PICTURE 2 : - C, D
PICTURE 3 :- E, F, G
Mark each statement as True or False and justify your answer. a) The columns of a...
nsid r the following et ār vnctors. Let 1 v2 and V3 be column vectors in and let A be the 3 × 3 matrix v 1 v2 v③ with these vectors as its columns. The vi v2 and ] are linearly dependent if and nly the hom 9ene us linear system with augmented matrix 시 has a no tr ia solution Consider the following equation. 81-3-311 Solve for ci 2, andc3. If a nontrlvial solution exists, state it or...
Can I get help with questions 2,3,4,6?
be the (2) Determine if the following sequences of vectors vi, V2, V3 are linearly de- pendent or linearly independent (a) ces of V 0 0 V1= V2 = V3 = w. It (b) contains @0 (S) V1= Vo= Va (c) inations (CE) n m. -2 VI = V2= V3 (3) Consider the vectors 6) () Vo = V3 = in R2. Compute scalars ,2, E3 not all 0 such that I1V1+2V2 +r3V3...
Please answer me fully with the details. Thanks!
True of False? Justify yo ur answer. —D т. If {ii, .., in} is a linearly independent subset of (1) Let V bea vector spacе, аnd let dim(V) V. then n < т. (2) Let V and W be vector spaces, and suppose that T : V -+ W is a linear transformation. If there are vectors i, 2, ..., Tj in V such that the vectors T(),T(T2),...,T(vj) span W, then the...
(a) (5 points.) Let W CW CW CW3 be distinct subspaces of R? True/False (Justify your answers): (i) Wo must be the zero subspace. (ii) W, must be R. (iii) W, must be RP. (iv) Suppose V1, V2, V3 are vectors such that vi EWW -for each 1 <i<3. Then {V1, V2, V3} must be a basis for R. (v) There are three linearly independent vectors in R that do not form a basis for R?
please give the correct answer with explanations, thank you
Let S {V1, V2, V3, V4, Vs} be a set of five vectors in R] Let W-span) When these vectors are placed as columns into a matrix A as A-(V2 V3 r. ws). and Asrow-reduced to echelon form U. we have U - -1 1 013 001 1 state the dimension of W Number 2. State a boss B for W using the standard algorithm, using vectors with a small as...
3. [1 mark each] Determine which of the following statements are true and which are false. (a) The inverse of a rotation matrix (Rº) is (R-8). (b) If the vectors V1, V2, ..., Vk are such that no two of these vectors are scalar multiples of each other then they must form a linearly independent set. (c) The set containing just the zero vector, {0}, is a subspace of R”. (d) If v, w E R3 then span(v, w) must...
I am looking for how to explain #4 part b. I have gotten the
matrix A and I believe the answer is W = span{ v1 u2 u3 } however
I'm not really sure if that is correct or not. Please give a small
explanation. Also im not sure if I need to represent the vectors in
A as columns or rows, or if either one works.
For the next two problems, W is the subspace of R4 given by...
1) Determine if w is in the subspace spanned by v1, v2,
v3
2) Are the vectors v1, v2, v3 linearly dependent or
independent? justify your answer
Question 2. (15 pts) Let vi=(-3 0 6)", v2= (-2 2 3]", V3= (0 - 6 37, and w= [1 11 9". (1). Determine if w is in the subspace spanned by V1, V2, V3. (2). Are the vectors V1, V2, V3 linearly dependent or independent? Justify your answer
Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 01 0 - 1 3 1 1 -6 2 1 - 12 Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that...
please answer the following question with detailed step
1 1. Consider vi = 2 V2 = a and v3 = -1 (a) Find the value(s) of a such that 01,02 and v3 are linearly dependent and write Vi as a linear combination of v2 and 03, if possible. (b) Suppose a = 0, write v = 2 as a linear combination of v1, V2 and 03. (c) Suppose a = 0, use the Gram-Schmidt process to transform {V1, V2, V3}...