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Author: nsharp1
No. Questions: 3
Created: Sep 4, 2019
Last Modified: 5 years ago

Matrices and Data Manipulation

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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

A.

Which of the following operations would result in a 2-by-2 matrix, with only the first and third points as elements? Let this matrix be called B.

$B = [[1,0,1,0,0],[1,0,1,0,0]] A$
$B = A [[1,1],[0,0],[1,1],[0,0],[0,0]]$
$B = A [[1,0],[0,0],[0,1],[0,0],[0,0]]$
$B = [[1,0,0,0,0],[0,0,1,0,0]] A$

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

B.

Which of the following operations would create a matrix, called C, where each element is the difference of the respective coordinates of the two points? I.e., the first element is the difference of the two x-coordinates.

$C = B[[1,-1]]$
$C = [[1,-1]] B$
$C = [[1],[-1]] B$
$C = B [[1],[-1]]$

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

C.

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).

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