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 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: 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.

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A: A vector is written as aî + bĵ.

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

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A: Solution is given below:-

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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…

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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.