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sesenic [268]
3 years ago
11

If B is a basis for a subspace H, then each vector in H can be written in only one way as a linear combination of the vectors in

B. The dimension of Nul A is the number of variables in the equation Ax = 0. The dimension of the column space of A is rank A. If B = {vi,...,Vp} is a basis for a subspace H of Rn, then the correspondence makes H look and act the same as Rp. If H is a p-dimensional subspace of Rn, then a linearly independent set of p vectors in H is a basis for H.
Mathematics
1 answer:
mixas84 [53]3 years ago
4 0

Answer:

Step-by-step explanation:

STEP 1 It's true

If H is a p-dimensional subspace of Rn, then B must be a set of p elements {v1, v2, . . . , vp}. To represent any vector b in H is to find the coefficients cj in the linear combination

b = c1v1 + c2v2 + . . . + cpvp

of vectors in B whose sum is b. This is equivalent to solving a system of equations with p equations and p unknowns. Because the vectors are linearly independent by the definition of a basis, this means there can only be one solution.

STEP 2 It's true

The dimension of Nul A is the number of free variables in the equation Ax = 0.

STEP 3 It's true

The rank of a matrix A is equal to the dimension of Col(A).

STEP 4 It's true

Because H is a p-dimensional subspace of Rn, any linearly independent set of exactly p elements in H is automatically a basis for H, hence also spans H

STEP 5 It's true

This correspondence is a one-to-one correspondence between H and Rp that preserves linear combinations, this is also known as an isomorphism. Because H is isomorphic to Rp, H looks and acts the same as Rp even though the vectors in H themselves may have more than p entries.

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Write f(x) = 2x2 – 44x 185 in vertex form. To write f(x) = 2x2 – 44x 185, factor out from the first two terms. Next, form a perf
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The quadratic function f(x) = 2x² – 44x + 185 is written in vertex form is f(x) = 2(x –  11)² – 57.

<h3>What is a quadratic equation?</h3>

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The quadrattic equation is f(x) = 2x² – 44x + 185.

Take common 2 from the equation, we have

f(x) = 2(x^2 - 22x )+ 185

Add and subtract 121, we have

f(x) = 2(x^2 - 22x +121 - 121 )+ 185\\\\f(x) = 2[(x^2 - 11)^2-121]+ 185\\\\f(x) = 2(x-11)^2 - 242 + 185\\\\f (x ) = 2(x-11)^2 -57

And we know that the standard equation

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The vertex (h, k) is (11, -57).

More about the quadratic equation link is given below.

brainly.com/question/2263981

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There are a total of 84 students in a robotics club in the science club. The science club is 12 more students in the robotics cl
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Answer:


Step-by-step explanation:

Let the Number of students in the Robotics club be x

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So ,

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combining the like terms we get

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Divide both sides by 2

x=36

So ,


Number of students in the Robotics club = 36

Number of students in the Science club =36+12 = 48



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Answer:

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