Understanding Scalar Multiplication and Dilation

The video tutorial explains scalar multiplication and its role in transforming a matrix. It describes how matrix elements can be viewed as coordinates on a plane, leading to the formation of a triangle. The concept of dilation is introduced, showing how scalar multiplication affects the size of shapes without altering their form. The tutorial demonstrates performing scalar multiplication on a matrix and compares the original and transformed triangles, highlighting the effects of different scale factors.

What is scalar multiplication in the context of matrices?

• Dividing each element of the matrix by a constant

• Multiplying each element of the matrix by a constant

• Adding a constant to each element of the matrix

• Subtracting a constant from each element of the matrix

How can the elements of a 2x3 matrix be interpreted in a coordinate plane?

• As angles of a triangle

• As areas of rectangles

• As coordinates of points

• As distances between points

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CCSS.5.G.A.2

What does each column in the matrix represent when plotted on a coordinate plane?

• A line segment

• A point

• A vector

• A circle

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CCSS.8.G.A.3

What happens to a shape when it undergoes dilation?

• It reflects

• It becomes smaller or larger without changing shape

• It rotates

• It changes its shape

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CCSS.8.G.A.3

What is the effect of a scalar between 0 and 1 on a shape?

• The shape reflects

• The shape gets smaller

• The shape gets larger

• The shape rotates

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CCSS.8.G.A.3

What is the scale factor used in the dilation described in the video?

• 1/2

• 3/4

• 4/5

• 2/3

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CCSS.HSN-VM.B.5B

CCSS.HSN-VM.B.5A

What is the result of multiplying the x-coordinate 8 by the scalar 3/4?

• 4

• 6

• 8

• 10

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CCSS.7.RP.A.3

What is the new y-coordinate when -4 is multiplied by 3/4?

• -1

• 0

• -2

• -3

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CCSS.7.NS.A.2A

What is the new x-coordinate when -6 is multiplied by 3/4?

• -3

• -4

• -9/2

• -5

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CCSS.8.G.A.3

What is the effect of a scalar greater than 1 on a shape?

• The shape reflects

• The shape rotates

• The shape gets smaller

• The shape gets larger

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CCSS.8.G.A.3