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# I need help with Matrices please

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Consider the matrices.

L = [2     -3]    ,    M= [ -1     7]    ,   N= [-8 -2]    ,    P= [0   0]    and    Q= [-6]
1     2                   -2      -6              1   4                 0    0                     -8

2      -3               3   9

-1     10              2   -7

What operations are defined for these matrices?

fill in the blanks of what options correctly fit the title (Operation is defined) or (Operation is not defined ) :

Operation is defined     Operation is not defined

__________________

OPTIONS:

a.) N     b.) M - N    c.) P    d.) M + P

Aug 18, 2023

#1
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To determine whether an operation is defined or not for two matrices, we need to check whether the matrices have the same dimensions (same number of rows and columns) so that the operation can be performed. Let's analyze each option:

a.) L - N: Matrix L is a 2x2 matrix and matrix N is a 3x2 matrix. Since the number of columns is different, the operation is not defined.

b.) M - N: Matrix M is a 2x2 matrix and matrix N is a 3x2 matrix. Again, the number of columns is different, so the operation is not defined.

c.) Q + P: Matrix Q is a 1x1 matrix (scalar) and matrix P is a 2x1 matrix. The number of columns is different, so the operation is not defined.

d.) M + P: Matrix M is a 2x2 matrix and matrix P is a 2x1 matrix. The number of columns matches, so the operation is defined.

Based on the analysis:

Operation is defined (d.) M + P)

Operation is not defined (a.) L - N), (b.) M - N), (c.) Q + P)

Aug 18, 2023
#2
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Let \(M_1\) and \(M_2\) be arbitrary matrices with \(r\) rows and \(c\) columns. The operation of addition or subtraction of matrices is defined if and only if \(r_{M_1} = r_{M_2}\) and \(c_{M_1} = c_{M_2}\). I will do the first few, and you should be able to do the rest.

a) \(L - N\)

\(L\) is a 2x2 matrix, which means that L has 2 rows and 2 columns. N is a 4x2 matrix, which means that it has 4 rows and 2 columns. The numbers of rows is different. Therefore, \(L-N\) is not a defined operation.

b) \(M-N\)

\(M\) is a 4x2 matrix, which means that M has 4 rows and 2 columns. N is a 4x2 matrix, which means that it has 4 rows and 2 columns. The number of rows and the number of columns are the same. Therefore, \(M - N\) is a defined operation.

You should be able to complete the next two. Let me know if you have any questions about it.

Aug 19, 2023
#3
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The following are the possible operations for matrices:

Addition: Two matrices can be added if they have the same dimensions.

Subtraction: Two matrices can be subtracted if they have the same dimensions.

Multiplication: Two matrices can be multiplied if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Scalar multiplication: A matrix can be multiplied by a scalar.

Transposition: The transpose of a matrix is created by exchanging the rows and columns.

Based on the given matrices, we can see that:

L and N have the same dimensions (2x2), so L - N is defined.

M and N have the same dimensions (2x2), so M - N is defined.

Q and P are not the same dimensions (1x2 vs. 2x2), so Q + P is not defined.

M and P are not the same dimensions (2x2 vs. 1x2), so M + P is not defined.