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- Suppose the vectors u, v, x, y, z are distinct vectors in Rª, and that the vectors x, y, z are linearly independent. Which of the following are TRUE? (select all that apply) 0 The vectors x+y+z, x-y+z, x + z are linearly independent. The equation ax +by+cz = 0 has only the solution a = b = c = 0. The vectors x + y, y+z, x+z are linearly independent. One of the vectors in the set {x, y, z) can be expressed as a linear combination of the other two. Every vector in R4 can be expressed as a linear combination of the vectors x, y, z. The vectors u, v, x, y, z are linearly independent.arrow_forwardGiven the following vectors A=-4a+3a - 2a X y B=a +5a +7a_ y C=-2a-4a +6a X y 2 Evaluate |AX (BXC)|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_forward
- Please give both ans.arrow_forward1.The following problems will all make reference to these three vectors: 4 7 A= 4 B = 5 C= -1 -4 -5 a. Calculate the following dot products: Ä•B, Ã•Č¸ and B•(À+2č). b. Which vector (among A, B, and C) is the longest? Which is the shortest? C. Calculate the vector product Â×(B×ċ).arrow_forwardLet V1 -16 -8-8-8-8 -7 V3 -13 -4 -2 2 = 1. Is w in {V1, V2, V3}? Type "yes" or "no". -29 14 4. Is w in Span {V₁, V2, V3}? Type "yes" or "no". and w= 4 10 3 2. How many vectors are in {V₁, V2, V3}? Enter "inf" if the answer is infinitely many. 3. How many vectors are in Span {V₁, V2, V3}? Enter "inf" if the answer is infinitely many.arrow_forward
- 4. a, Determine whether vectors V and W are parallel, orthogonal, , or neither. If parallel determine whether they have the same directions or opposite directions V= -2i+3j ( 1= 2 6 v = 31-5j v=-2i + 3j W = -61 +9 (245) j w = 61 +10 j w = -6i-4 jarrow_forwardPlease provide me accurate solutions and explain each stepsarrow_forwardPlease help. This problem involves finding the value of a variable that would make a set linearly independent. Thank you.arrow_forward
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