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2 years ago

A recipe requires ¼ cup of milk for each ⅙ cup of cheese. How many cups of cheese are needed for each cup of milk?

Mathematics

1 answer:

Murrr4er [49]2 years ago

4 0

Answer:

2/3 cups of cheese

Step-by-step explanation:

1/4 cup of milk = 1/6 cup of cheese

1 cup of milk = 1 cup of milk x 1/6 cup of cheese

1/4 cup of milk

= 1 / 1

6 4

= 1 x 4

6 1

= 4/6

= 2/3 cups of cheese

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Matrices A and B are square matrices of the same size. Prove Tr(c(A + B)) = C (Tr(A) + Tr(B)).

alexira [117]

Answer with Step-by-step explanation:

We are given that two matrices A and B are square matrices of the same size.

We have to prove that

Tr(C(A+B)=C(Tr(A)+Tr(B))

Where C is constant

We know that tr A=Sum of diagonal elements of A

Therefore,

Tr(A)=Sum of diagonal elements of A

Tr(B)=Sum of diagonal elements of B

C(Tr(A))= $C\cdot$ Sum of diagonal elements of A

C(Tr(B))= $C\cdot$ Sum of diagonal elements of B

$C(A+B)=C\cdot (A+B)$

Tr(C(A+B)=Sum of diagonal elements of (C(A+B))

Suppose ,A= $\left[\begin{array}{ccc}1&0\\1&1\end{array}\right]$

B= $\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]$

Tr(A)=1+1=2

Tr(B)=1+1=2

C(Tr(A)+Tr(B))=C(2+2)=4C

A+B= $\left[\begin{array}{ccc}1&0\\1&1\end{array}\right]+\left[\begin{array}{ccc}1&1\\1&1\end{array}\right]$

A+B= $\left[\begin{array}{ccc}2&1\\2&2\end{array}\right]$

C(A+B)= $\left[\begin{array}{ccc}2C&C\\2C&2C\end{array}\right]$

Tr(C(A+B))=2C+2C=4C

Hence, Tr(C(A+B)=C(Tr(A)+Tr(B))

Hence, proved.

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