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3 years ago

5

without doing any calculations or modeling, explain how you know that the 24 inch by 32 inch mirror and the 20 inch by 32 inch m

irror are not similar. Explain

1 answer:

uysha [10]3 years ago

6 0

They are not similar because they don’t have the same dimensions and therefore are not the same shape

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3 years ago

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3 years ago

Which of the following is a perfect square.<br>A.127<br>b.100<br>c.102<br>d.13

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3 years ago

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The n × n identity matrix is the matrix with diagonal entries are all 1’s and the rest are all 0’s. Show that, for any n×n matri

Tatiana [17]

Express the matrix $I$ like $(\delta_{ij})_{n\times n}$ , where $\delta_{ij}=1$ if $i=j$ and $\delta_{ij}=0$ if $i\neq j$ . ( $\delta_{ij}$ is known as kronecker's delta)

In the same form we express the matrix $A=(a_{ij})_{n\times n}$ .

The firs index indicate the row and the second the column.

By the multiplication of matrices we have $AI=(c_{ij})_{n\times n}$ , where

$c_{ij}=\sum_{k=1}^n a_{ik}\delta _{kj} = a_{ij}$

because only $\delta_{jj}$ is non-zero in the last sum.

therfore we have $AI=(c_{ij})_{n\times n}=(a_{ij})_{n\times n}=A$ .

In the same manner we have

$IA=(d_{ij})_{n\times n}$ , where

$d_{ij}=\sum_{k=1}^n \delta _{ik}a_{kj} = a_{ij}$

And so, $IA=A$

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3 years ago