For Problem 16-18, determine whether the given set of
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- Solve for X in the Equation, given A=-401-532 and B=12-2144 a 3X+2A=B b 2A5B=3X c X-3A+2B=0 d 6X4A-3B=0arrow_forward1. Write the vector H- 16 as a linear combination of the vectors and Darrow_forward1. Find all solutions: 2. In what ways can 88-8 and be written x+y ==0 a as a linear combination of [] [] [4], and ² 3. Show that the vector 2 is NOT contained in the span of the following three vectors 6 4. For which b are the vectors -0.0 x+2y+z=5 2x+3y-z=3 independent?arrow_forward
- Let -0-0-0-0 V2 = w= -5 = -2 = = If possible, express w as a linear combination of the vectors V₁, V2 and v3. Otherwise, enter DNE. For example, the answer w = 4v₁ + 5v2 + 603 would be entered 4v1 + 5v2 + 6v3.arrow_forwardIf k is a real number, then the vectors (1, k), (k, k+ 56) are linearly independent precisely when k # a, b, where a = , 6 = and a < b.arrow_forwardIf the vector v= -8 can be written as a G- 3 linear combination of v, and -3 V2 2 such that -3 v= a, v, +a2 V2 - Which of the following is the value of a, ? O 2 O 5 handwritten only O -2 O -5 None of themarrow_forward
- The vectors -3 -3 -9 w 3= 12 20 + k 15 are linearly independent if and only if k +arrow_forwardSuppose that A= 2 6 2 [-1 1 1] Describe the solution space to the equation Ax = 0. Describe the solution space to the equation Ax = b where b : Are there any vectors b for which the equation Ax = b is inconsistent? Explain your answer. Do the columns of A span R? Explain your answer.arrow_forwardFor each of the following lists of vectors in R3, determine whether the first vector can be expressed as a linear combination of the other two. (a) (-2,0,3) ,(1,3,0),(2,4,-1) (b) (1,2,-3) ,(-3,2,1) ,(2,-1,-1) (c) (3,4,1) ,(1,-2,1), (-2,-1,1) (d) (2,-1,0) , (1,2,-3), (1,-3,2) (e) (5,1,-5) , (1,-2,-3), (-2,3,-4) (f) (-2,2,2) ,(1,2,-1) ,(-3,-3,3)arrow_forward
- If the answer to (a) is yes, express the following two vectors each as linear A Given the following two vectors I=and V2 Are these two vectors linearly independent? 1. combination of UrL and Usarrow_forwardFor what values of c are the vectors t + 3 and 2t + c2 + 2 in P1 linearly independent?arrow_forwardIf v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.arrow_forward
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