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- Express each of the following vectors in R² as linear combinations of the vectors [3] and [3] (a) (b) (c) (d) 7 13 H 5 5 12 22 = || = = + + + + + 5 r 3 rarrow_forwardGiven x=(1,-2,-1,a) and y=(3,3,-2,1) are two 1x4 row vectors, where "a" is some constant, which of the following statements is false? O y-2x = (1,7,0,-2a) x· 2y =a – 1 x and y are orthogonal if a=1. Ilx||=/6+a?arrow_forwardProblem #9: Given three linearly independent vectors V₁ = (-9,3,-9,9,-2), V2 = (-8, 10, 9, -3, 10), V3 = (-7,-9,-7, -7,0), in R5, complete this to a basis using the first two standard basis vectors which work. If the first two standard basis vectors that work are e, and ej then enter the values of i and j into the answer box below, separated with a comma. Problem #9:arrow_forward
- Solve the following two problems. You can use your calculator or MATLAB, but you will need to justify your argument and conclusions 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0,-1] in R. Decide whether they are linearly independent.arrow_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_forwardProblem 6. Prove that the vectors v₁ = (1, 0, -1), U₂ = (1, 2, 1), V3 = (0, -3,2) form a basis for R³. Express each of the standard basis vectors, (1, 0, 0), (0, 1, 0), and (0,0,1) as a linear combination of v₁, U2, U3.arrow_forward
- The following question is from linear algebra first year: Factors the vector (6, -5, -1)t into three components a,b,c that satisfy the following conditions: a depends on (2,0,1)t, b depends on (1,2, 0)t and c is orthogonal to a and b. Please show it step by step. Can we get integers as answers?arrow_forwardIf k is a real number, then the vectors (1,k),(k,7k+8) are linearly independent precisely when k ≠ a,b, where a = ? and b = ?, and a<barrow_forward1. Write the vector H- 16 as a linear combination of the vectors and Darrow_forward
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