Suppose a1, a2, ag, a4, and ag are vectors in R°, A = (a1 a2 a3 a4 ag), and 1 0 0 -5 41 rref(A) =|0 1 0 0 0 1 -2 2 1 a. Select all of the true statements (there may be more than one correct answer). OA. span{a1,a2, ag} = R OB. {a1, a2, a3} is a basis for R* Oc. {a1, a2, a3, a4} is a basis for R OD. span{a1, a2, ag, a4} = R³ OE. {a1, a2, a3, a4} is a linearly independent set OF. {a1, a2, as} is a linearly independent set OG. {a1, az} is a linearly independent set OH. {a1, az} is a basis for R Ol. span{a1, az} b. If possible, write ag as a linear combination of a1, a2, and a3 otherwise, enter DNE. a4 c. The dimension of the column space of A is , and the column space of A is a subspace of d. Find a basis for the column space of of A. If necessary, enter a1 for a,, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4,5>. Enter your answer as a comma separated list of vectors. A basis for the column space of A is { } e. The dimension of the null space of A is and the null space of A is a subspace of f. If x1 = (5, 2,-1,1,0), then Ax1 Is x1 in the null space of A? choose v

Q: would the two vectors be (1 1 1 0) and then (0 0 0 1)?

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Q: Consider the vectors: å = ỉ– 3j + 2k , b' = 4j – 2k and ở = i + k in 3D A. Write 3a – 4 b - 2¢ in a…

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Q: Calculate [1, 2, 2] x [5, -5, -1] -

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Q: The nullspace of A = the values of i and j. i= j= -6 9 -3 -4 6 321 can be written as the span of the…

A: Let A be a matrix of order m*n , then  The null space of A is defined as Nul(A)={ x in Rn : Ax=0 } .

Q: Which of the following represents a combination of vectors to form ED as a resultant? C Ra Bran B…

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Q: Consider the following vectors: 2 4 3 8 -3 c²= -8 -3 3 7 For each of the following vectors,…

A: Given that              a→=23-33, b→=48-85, c→=2-367

Q: Consider the vectors à = (5,3,7) and b = (2, -3,4). Answer or calculate each of the following.…

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Q: Consider the following vectors: -1 -3 -2 3 -3 4 8 For each of the following vectors, determine…

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Q: Consider the following vectors: 3 9 u= = [³₁] · V = [₁0] · W = [-₁0], x= []. V= W= -5 10 X ·

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Q: 9. If = 1, 4, 5) and W = (2, -3, 1 V ( − w a) 3-2W b) |v|

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Q: State if the following statement i O True O False true or false. The set of vectors B=(u= (2,7,3);…

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Q: State if the following statement is true or false. The set of vectors B={u=(2,7,3); v = (1,0,7) ;w =…

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Q: Let u be a vector. Select the most correct statement.A. The vector 4u could be longer or shorter…

A: The objective of the question is to understand the relationship between the vectors 4u and -5u.

Q: Given u = , v = -5i - j, and w (AB) is defined by the points (1, 6) and (-2, 8). a Find v in…

A: This is  a problem of vector. By dissolving vector in x and y parts we will convert it into…

Q: If v = –i + 2j and --Projw= w = -2i + 3k, then - اخترأحد الخيارات -9 52+ j.A C 2 .B - C. Zero vector…

A: Solution

Q: Which of the following vectors is a particular solution to the equation? -4 -3 -9 -2 51 v2 -6 -6 -6…

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Q: Suppose we know that Write A 6 as a linear combination of the vectors 5 8- 5 6 = 0 H + 6 1 1 -DE-B H…

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Q: What value of a will make the vectors (-2, x, 1) and (2, –1, 1) orthogonal? Select one: O a. 3 O b.…

A: For orthogonal, dot product of two vectors are zero.

Q: A vector is written as aî + bĵ. What form is that?

A: A vector is written as aî + bĵ.

Q: Let a = (8,-6,7) and b = (-1,4, -3) be vectors. Compute the following (the answers to A, B, C are…

A: Given vectors  a = &lt;8,-6,7&gt; b=&lt;-1,4,-3&gt;

Q: a. Find the coordinate vector for each vector in the figure. ■ā= b= ■ ■= b -6-5-4-3-2-1 OK 6 5 4 3 с…

A: Solution is given below:-

Q: e) Let C be a new base of R3. If the base change matrix, from base A to base C is - 10 55 32 35 -5 3…

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Q: Determine which of the following vectors are orthogonal to each other: 12 2 X = 3 X2 1 X3 -3 -5 3

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Q: "Given that 3 -4 = 5 -3+ 2 5 ܐ write 3 as a linear combination of the vectors -2 + 5 -3 -2 5 -4 1 2…

A: Here , a vector is given and now we have to represent it as a linear combination of three vectors .

Q: For each pair of vectors in i-iii, find the following: e. ||ū|| and ||3|| b. and ||ū|| |||| f. Ili2…

A: Since you have asked a question with multiple subpart here we will solve the first three subparts…

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

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.