For each of the following linear transformations L mapping R3 into R2, find a matrix A such that L (x) = Ax for every x in R3: (a) L ((x1, x2, x3)T ) = (x1 + x2, 0)

Step-by-step explanation:

We have a linear transformation L mapping R3 into R2 ⇒

⇒

We need to find a matrix A such that for every in R3

We have the formula of ⇒

We must notice that is a vector in R3 and the image of L is a vector in R2.

Given that L is define as ⇒ , the matrix that defines the linear transformation L will be a matrix A ∈

How can we find this matrix A? One way is to apply L to a base from the domain of L (R3) and putting that result as the columns of the matrix A.

Let's work with the cannonic base of R3  :

{ }

Now if we transform each vector of the base :

The final step is to put the result of each vector as the columns of the matrix A :

⇒

being A the matrix calculated. It is important to remark that the transformation L is defined in the cannonic base.

We can verify the matrix A by performing the transformation into any vector of R3. For example, let's calculate :

If we use the equation and :

If we use the matrix A calculated.

answer:

step-by-step explanation:

here, the total dishes = 10

dishes having meat = 3 ( chicken, meatloaf and hamburger )

thus, the probability of having meat on the chosen dishes = number of dishes having meat / total dishes

=

therefore, the probability of not having meat = 1- the probability of having meat on the chosen dishes

=

=

=

⇒ option b is correct.