Yvette encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, she multiplied the clear text 5 2
code for each letter by the matrix
to get a matrix that represents the encoded text. The matrix representing the
2
48
73
114 30 136 78 35
encoded text is
What is the secret phrase? Determine the location of spaces after you
21
32
50
13
68
35 15
decode the text.
FIND THE PRODUCT
FIND THE INVERSE
FINE IS THE PIANO
FINE IS A WARM DAY

below

Step-by-step explanation:

Assuming the matrix which multiplies the clear text code is:

    |-3   2|

C =|-4   3|

And the matrix re<presenting the encoded text is :

    |10  -26  -49  9  3  -13   -50|

B = |16  -33  -63  16  9  -10  -65|

Calling X the secret message, the relationship between the 3 matrices can be represented as:

C*X = B  

Solving for X:

X = C^-1*B

where C^-1 is the inverse of C.  

        |-3   2|

C^-1 =|-4   3|

Multiplying:

    |2       12 21 5 9 19 20 |

X = |8 5 7 12 15 22 5 |

Replacing numbers by its corresponded letter (see picture attached):

    |B L  U E I S T |

x = |H E G L O V E |

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source:

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .