determine whether the first vector is in the subspace of R3 generated by the other vectors. 1) (1, 4, -3); (1, 0, 1), (1, 1, 0), (3, 1, 2) 2) (1, 1, 2); (0, 1, 0), (3, 5, 6), (1, 2, 1)

Q: Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span.…

A: a) Suppose that    be  a  basis  of      Then, which is  a  contradiction.    Hence, is  not a…

Q: M2,2 is the vector space of all 2 x 2 matrices. List the o element of this vector space.

A:

Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

A:

Q: Find a basis for the subspace of R* spanned by S. s 3D {(2, 5, -3, -2), (-2, -3, 2, -3), (1, 3, —2,…

A:

Q: which of the following are subspaces of R3 provide typed answer

A: To determine which of the following area subspaces of R3. (A) All vectors of the form (a,0,0) (B)…

Q: False/True: If vectors V1, V2, ..., Un span the subspace V, then every vector in V can be written as…

A:

Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

A:

Q: Determine if all polynomials P = ao + a,x + a,x² + a3x³ , with ao, a1, a2, az integer, is subspace…

A:

Q: Which of the following sets of vectors in P2 are linearly dependent? (a) 2-x+4x?, 3+6x +2x², 2 + 10x…

A: (a) given set of vectors  we shall  write in matrix form  A= 2-14362210-4if rank of above matrix is…

Q: Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 1, O),…

A: We have to find a basis for the subspace of R³ that is spanned by the given vectors.

Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: (-9,6) Use matrices to reflect the vector the line y = x. ove

A: Topic:- algebra

Q: 9. Determine whether the vectors v₁ = (1,1,2), v₂ = (1,0,1) and v3 = (2,1,3) span the vector space…

A: We know that the dimension of vector space  is 3.If the given three vectors are linearly…

Q: Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a +…

A: To Find: Basis for the subspace of R2  of the form (a,b,c,d) such that c=a+7b and d=a-6b

Q: Determine whether W is a subspace of V

A:

Q: Find a basis for the orthogonal complement of the subspace of R spanned by the vectors. v1 = (1,5,…

A:

Q: 5. Determine if the vectors x² + x, 2x²,2x − 3, 9 in P3 are linearly independent or linearly…

A: In this question, we will check the given vectors is linearly independent or dependent.

Q: Let H ={ E : ab,cER), which is a subspace of the vector space of all2x2 matrices. Let B = (: 4which…

A:

Q: Find a basis for the subspace of R" spanned by S. S = {(43, -21, 6, 18), (-14, 7, -2, -6), (6, –3,…

A: Subspace of  ℝ4  spanned by S is               S = { (43,-21,6,18) ,(-14,7,-2,-6) ,…

Q: Let M,xn be a set of square n x n-matrices. Is the set M„xn a vector Explain. Find 2 different bases…

A: We have to solve given problem:

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.