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Evaluate

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Evaluatea three by two matrix with row one: 4, 5: row two: negative 2, 1; and row three: 3, 0; times a two by three matrix with row one: 1, negative 2, 1; and row two: 0, 3, negative 4a three by two matrix with row one: 4, 5: row two: negative 2, 1; and row three: 3, 0; times a two by three matrix with row one: 1, negative 2, 1; and row two: 0, 3, negative 4.
A. a three by three matrix with row one: 4, negative 10, 5; row two: negative 2, 3, negative 20; and row three: 0, 0, 0
B. a three by three matrix with row one: 4, 7, negative 16; row two: negative 2, 7, negative 6; and row three: 3, negative 6, 3
C. a three by three matrix with row one: 4, 7, negative 16; row two: negative 2, 7, negative 6; and row three: 3, negative 3, negative 1
D. a three by three matrix with row one: 4, 7, negative 16; row two: negative 1, 7, negative 6; and row three: 3, negative 6, 3

 

asked Sep 5, 2014 in ALGEBRA 2 by tonymate Pupil

1 Answer

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Best answer

Multiplication of two matrices is possible if the number of columns in the

first matrix equals the number of rows in the second matrix.

Let A be the first matrix and B be the second matrix.

The dimensions of the first matrix A are 3×2, so the number of the columns

in the first matrix is 2.

The dimensions of the second matrix B are 2×3, so the number of the rows

in the second matrix B is 2.

The number of columns in the first matrix equals the number of rows in the

second matrix. So, matrix product is possible and its dimensions are 3 ×3

Let P be the matrix product.

image

The product matrix is image.

So option B is correct.

answered Sep 5, 2014 by bradely Mentor
selected Sep 5, 2014 by tonymate

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