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Type: Multiple-Choice
Category: Matrices
Level: Grade 12
Standards: HSN-VM.C.6
Author: nsharp1
Created: 5 years ago

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The following matrix, A, lists 5 sets of points, where the first column is the x coordinate and the second column is the y coordinate.

$A = [[3,2],[4,1],[5,9],[7,-1],[1,8]]$

The following questions will use matrix operations to find the distance between the first and third points.

Grade 12 Matrices CCSS: HSN-VM.C.6

The transpose of a matrix is when the rows and columns are switched. For a given matrix,

$M$ , and its transpose,

$M^T$ , the columns of

$M$ correspond to the rows of

$M^T$ . This means that the dimensions of the matrix are switched; a 2-by-4 matrix becomes a 4-by-2 matrix. For a 1-by-n or m-by-1 matrix, the single column becomes a single row (or vice-versa).

Which of the following operations would result in a matrix of only one element which is the square of the distance between the first and third points in the original matrix A? (Taking the square root of this element would therefore give the distance between these points).

$C^T C$
$C C^T$
$(C^T C)^2$
$(C C^T)^2$