Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R". The orthogonal projection y of y onto a subspace W can sometimes depend on the orthogonal basis for W used to compute y. Choose the correct answer below. O A. The statement is false. The uniqueness property of the orthogonal decomposition y = y +z indicates that, no matter the basis used to find it, the decomposition will always be the same. OB. The statement is true. For each possible orthogonal basis of W, y is expressed as a different linear combination of the vectors in that basis. O C. The statement is true. The orthogonal projection y of y onto a subspace W depends on an orthonormal basis for W. O D. The statement is false. The orthogonal projection y of y onto a subspace W depends on an orthonormal basis for W.

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

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A: To determine: The span of the following vectors geometrically. 123, 247

Q: Prove: If (ū. v} and ü, v. w} span the same vector space, then w is a linear combination of ū and v.

A: If {u⇀,v⇀}  and {u⇀,v⇀,w⇀} spans vector space V then,we will have to prove that we can write w as a…

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A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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Q: The vector -3 (GIE) -1 -4 0 -7 vectors -3 2 belongs to the span of the 5 Select one: O True O False

A: Given: W=span-3-10, -1-4-7. To check v=-325∈W.

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Q: Use vectors u= (-3, 1), v= (3, -3), and w= (0, 8) to find v (w+u), and determine whether the result…

A: Answer is given below

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.