Proof that R3 = W1 ⊕ W2, where W1 = {(x1, x2, x3) : x1 + x2 + x3 = 0} and W2 = Lin(1, 1, 1). Lin - space

Q: Show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2,…

A: We have to show that the function below is not an inner product on R3, where u = (u1, u2, u3) and v…

Q: V₁ = M 0 , V₂ = 1 and V3 = 11 0 -5 [3] เย เย Use the Gram-Schmidt procedure to produce an orthogonal…

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Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: Let f:R → R such that f(x) = x² – 2x + 1. Verify whether f is bijective ? explain your answer.

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Q: assume that Pr[A]=0.25Pr[A]=0.25, Pr[B]=0.35Pr[B]=0.35, and Pr[A∩B]=0.1Pr[A∩B]=0.1. 1)Pr[A|B] =…

A: Given: P(A) =0.25 P(B)=0.35 P(A∩B) =0.1

Q: Advanced Math Question

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Q: Let V = span{e2", xe2", x²e?=}. (a) Show that (a1e2a + a2xe2" + a3x²e2") e V for any a1, a2, az E R,…

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Q: Example 9. Classify each relation as constant, linear, quadratic, or neither. a) y = x² + 5x + 6 b)…

A: The solution is given below:

Q: Justify wether the following is an inner product or not =5x1y1-x1y2-x2y1+2x2y2 where x=(x1,x1) and…

A: By using axioms of inner product we have to show whether <x, y> is an inner product or not.

Q: Fact: Z is a Euclidean Domain. What is a norm? Fact: R is a Euclidean Domain. What is a norm' Is Q a…

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Q: |(u+ v) x (u – v)I = 2|u x v|

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Q: 4 -1 33. The dimension of the nul-space of A = 3 3 is 2 1 1 2 3 (A) 1 (B) 2 (C) 3 (D) 0 (E) 4 142 13

A: Given matrix A=5214−14332211123 We have to find the dimension of null space. For dimension of null…

Q: Discrete Math Show that f(x) = 3x - 5 is a bijection

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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.