Let M2x3(C) be the vector space of 2 x 3 matrices over C, with the usual rules of addition and scalar multiplication, and also view C as a vector space over C with the usual rules. a12 a13 Let T : M2x3(C) → C be the map H a12- a21 a22 a23 Show that T is linear.

Q: a) Find all values of a so that polynomials f = 4t-a and g = 5t-6 are linearly dependent in P₁.…

A: We can find the value of 'a' for which the given polynomial is linear dependent.

Q: Let V be the vector space of real 2 × 2 matrices with inner product (A|B) = tr(BtA). Let U be the…

A: Now , V=abcd:a,b,c,d ∈IRbe the Vector spaceof 2×2 real matricesendowed with the inner…

Q: Let V be a vector space of 2 × 2 matrices 2 4 over R. Let A 6. 2 6. -2 and C = 2 -10 В 4 Then the…

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Q: Consider the vector space P, of polynomials with real coefficients of degree at most two together…

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Q: Find a non-zero vector in Nul A and a non-zero vector in Col A for the following matrix: 1 2 4 5 -5…

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Q: Let A = and B = {b1.b2.b3} be bases for a vector space V, and suppose a, = 5b, - b2, az = - b, + b2…

A: Bases of a vector space

Q: Given a a vector in linear space V, check whether the following operations are linear…

A: Let V and W be vector spaces over the same field F. A mapping T:V →W is said to be a linear…

Q: Consider the 2 X 2 matrices A1 = 1 1 A2 = 0 1 A3 = 0 0 A4 = 1 0 1 1 1 0 () Argue whether these four…

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Q: Determine if S=R (real numbers) where -1 is not included, is a vector space with the operations:…

A: Vector space

Q: Determine whether the set of all matrices of the form (:: ;). a bc 1o), where a+e 0, and b +d+f 0,…

A: Given: abcdef , a+c=0, b+d+f=0

Q: Consider the 2 X 2 matrices A1 =  1      1           A2 =  0      1        A3  =   0      0      A4…

A: Thus, the four matrices are not linearly independent.

Q: Abe 21. ff sin²x dA, D D is bounded by y = cos x, 0≤x≤ π/2, y = 0, x = 0

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Q: Let B = Since the coordinate mapping determined by B is a linear transformation from R² into R²,…

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Q: Let V be the vector space of real 2 × 2 matrices with inner product  (A|B) = tr(B tA).  Let U be the…

A:

Q: Let x and a be vectors in R2 Define the L: R2→ R2 by L(x) = x +a Is this function a linear operator?…

A: Linear operator should satisfy L:Rn→Rn  a) Lu+v=Lu+Lv         u,v∈Rn b)Lcu)=cL(u

Q: Explain why A = [43²] and B = [144] -1 -18 form a linearly dependent set of vectors in M22. (Solve…

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Q: Let S be the space of all complex vectors (x, y, z) such that y = z². Determine whether or not S is…

A: In the given problem we verify the properties of vector addition

Q: Let V be the vector space of real 2 × 2 matrices with inner product    (A|B) = tr(BtA).    Let U…

A: Let A∈skewsymm2 and B∈symm2 Then  A,B=trBtA=trAtB , since A,B=B,A=tr-AB=-trBA=-trBtA ,since B∈symm2…

Q: If scalar multiplication and addition is redefined on R² in the following way, show that it is NOT a…

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Q: 1.) Let V be the set of all 2x2 matrices A = [ such that the product abcd = 0,1 as the operation O…

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Q: c. Show that V, with respect to these operations of addition and scalar multiplication, is not a…

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Q: Is R2 a subspace of the complex vector space C²? Justify your Yes/No answer.

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Q: A curve in polar coordinates is given by: r = 9+ 4 cos 0. Point P is at 0 = a.) Find polar…

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Q: Let A be an m x n matrix and let b be a vector of length n. If A x = b is consistent then rank(A) =…

A: We can check whether the given statement is true or false.

Q: Let M be the vector space of 2 x 2 real-valued matrices. For M = [ a b c d] we define M# = [d b…

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Q: Let W be the subspace of the vector space of polynomials of degree 3 spanned by 2₁ = 1 + 3x - 2x² +…

A: (.)  Given , be the subspace of the vector space of polynomials of degree  spanned by ,and .(.)…

Q: Consider the vector space M consisting of all matrices of the form b } a c 3a +4b-3c where a, b, and…

A: Given that M is spanned by abc3a+4b-3c|a,b,c∈ℝ If -34-29/5122/5 is in M then it must be of the…

Q: w that the space V = {(x1, x2, x3) ∈F3

A: To prove that the space V=(x1, x2, x3)∈F3|x1+2x2+2x3=0 forms a vector space.

Q: Find a basis of the subspace of R4 that consists of all vectors perpendicular to both Basis: 0 -3 9…

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Q: Show that if V is a real vector space and av=0, then a=0 or v=0

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Q: r projection oE the following

A: we've to show whether the projection operators are positive operators or not. Now a projection…

Q: Let V = M² X 2 (R) be the vector space of all real 2 x 2 matrices. Determine if the following…

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Q: Let A = {a₁,32,33} and B = {b₁,b₂,b3} be bases for a vector space V, and suppose a₁ = 5b₁ b₂, 1 a₂ =…

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Q: (2) an -1 Answer: Consider matrix A = scalar product w. y. [Please enter your answer numerically.…

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Q: Let V = R?, defined the addition by: %3D (u1 +u2) + (v1 + v2)= (U1 +V1 , U2 +V2 + 1) With standard…

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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.