(3) Is Mmxn(Q) is a vector subspace of Mmxn (R) over R?

Q: Is Mmxn(Q) is a vector space over R?

A:

Q: What is the dimension of the vector space M,x3R)?

A: SOLUTION-

Q: Express the vector == 7= Z+ y. -22] 10 as a linear combination of = -(-3) and y=

A: Consider the vector v→=-2210. To express it as linear combination of vectors x→=-4-5 and y→=1-5.…

Q: Determine if the set W of vectors (x1 , x2) in R such that xr? + x2 = 1 is a subspace of R’.

A: W is not a subspace of R²

Q: Determine whether the vector functions, x1(t)= [ et ]           [ -et ] and x2(t)= [ et ]…

A:

Q: Find the dimension of the subspace spanned by the given vectors

A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

Q: 4: Let H1 and H2 be two subspaces of R". Show that H1 n H2 is also a subspace of R".

A: To show a set W to be a subspace of the of a space X if a,b∈W then a+b∈W   and for a scaler λ and…

Q: If vector A = [4/1] and vector B = [-3/2] find A-B

A: Here two vectors A and B are given we have to find A-B.

Q: Find a vector G with curlG = sin xk.

A: Let F → = d1i+d2j+d3kThen curve F → =∇xF → =ijkddxddyddzf1f2f3Let us consider G→ = g1i+g2j+g3kThen…

Q: 4. Orthonormalize S (Gram-Schmidt). 5. Find the projection of v onto W.

A:

Q: Prove that the set of vectors of the form (a, b, c) where b = a +c is a subspace of R³.

A: According to the given information, it is required to prove that:

Q: Find the point on the line T = (-2, 2, 3) + t(4, 1, 1) that presents the shortest distance to the…

A:

Q: R? Which vector stretches the x + y = 0 subspace of ? Why is that? a. (2,1) b. (0,0) c.(1, -1)…

A:

Q: () S = and v = 3 1. Find the cosine of the angle between the first two vectors in S. 2. Find the…

A: According to the given information, Consider the set S:

Q: Let H be the set of all points in the third quadrant in the plane V = R². That is, H = {(x, y) | x <…

A:

Q: Let W be the subspace spanned by the u's. Write y as the sum of a vector in W and a vector…

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Q: Let W be a subset of the vectors in R where W = X2 X4 -x3 = x, - x, }. Show that W is a X3 3. X4…

A: We will use the formal definition of a subspace of a vector space to prove that, W is a subspace of…

Q: 5. Let H = {x E R³| x1 + x2 + X3 = 0}. Prove that H is a subspace of R3.

A:

Q: The set of all vectors in R squared  that satisfy 3x+4y=1 is a subspace of R squared . True False

A: 1. The set of all vectors in R squared that satisfy  3x+4y=1  is not a subspace of R squared.  i.e.…

Q: True/False: If V is a subspace of R", then dim(V) + dim(V+) = n. True False

A: This is true and follows from a famous theorem in linear algebra.

Q: Is (x > 0, y < 0) a subspace? Explain.

A:

Q: 3) Find a basis for the subspace of R that consists of the intersection of the planes X-3Y = 5Z and…

A: This is a problem of vector space.

Q: Prove the two Scalar Multiple Rules for vector functions.

A:

Q: 1,3x-2 4. Determine whether the veltors X-I and X²-3x+2 dve lihearly independent or dependent in Pz…

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Q: 7) Find all vectors v in F such that 2v + ) -)

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Q: If v is in R°, then the set of vectors a with v x a = 0 is a subspace.

A:

Q: X1 - X₂ = 0 = 0 X3 X4 = 0 X2 - 2x3 -

A: