Algebra II - Unit 1 Test Review

A triangle is located on a three-dimensional coordinate plane. Matrix A shows the location of each vertex, where the first column represents the x coordinate, the second column represents the y coordinate, and the third column represents the z coordinate.

The triangle is dilated by a scale factor of 2, then translated by the factors in matrix B, resulting in an image triangle as represented by the equation 2A + B.

In which directions are the vertices translated, as indicated by matrix B?

• 3 units in the x direction, -2 units in the y direction, 1 unit in the z direction

• 3 units in the x direction, 3 units in the y direction, 3 unit in the z direction

• 4 units in the x direction, 0 units in the y direction, 2 unit in the z direction

• 4 units in the x direction, 6 units in the y direction, 5 unit in the z direction

 $What\ is\ Y\ if\ X\ -\ 2Y\ =\ Z?$  

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Which matrix equation can be used to solve the systems of equations below?

3x - 2y = -3

6x - 5y = -9

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What is the value of the element in row 1, column 1 of matrix X?

• $\frac{-3y}{4}$

• 4

• 8y

• 0

Matrices X and Y both measure 2 x 2 and are inverses of each other. Which matrix represents their product?

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Which value of D would make the equation true?

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Given matrices G and H below, which statement is true?

• Matrices G and H are not inverses of each other because G + H not = I.

• Matrices G and H are not inverses of each other because GH not = I.

• Matrices G and H are inverses of each other because GH = I.

• Matrices G and H are inverses of each other because G + H = I.

Calvin encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code for each letter by the matrix C to get a matrix that represents the encoded text. The matrix representing the encoded text is above . What is the secret phrase? Determine the location of spaces after you decode the text.

• MY COLOR IS GREEN

• BLUE IS THE COLOR

• GREEN IS MY COLOR

• THE COLOR IS BLUE

Amir encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code for each letter by the matrix C to get a matrix that represents the encoded text. The matrix representing the encoded text is above. What is the secret phrase? Determine the location of spaces after you decode the text.

• THE BEAN IS GREEN

• BLUE IS THE GLOVE

• GREEN IS THE BEAN

• THE GLOVE IS BLUE

If K, then what is –K?

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