Math  /  Algebra

QuestionPerform the given operation (if defined, if not enter DNE) on the matrices. A=[432404],B=[505553],C=[510433]BC=\begin{array}{l} A=\left[\begin{array}{ccc} -4 & 3 & -2 \\ 4 & 0 & 4 \end{array}\right], B=\left[\begin{array}{cc} -5 & 0 \\ 5 & 5 \\ 5 & 3 \end{array}\right], C=\left[\begin{array}{ll} 5 & -1 \\ 0 & -4 \\ 3 & -3 \end{array}\right] \\ B-C= \end{array}

Studdy Solution

STEP 1

1. The operation to be performed is matrix subtraction.
2. Matrix subtraction is defined only if the matrices have the same dimensions.

STEP 2

1. Verify the dimensions of matrices B B and C C .
2. Perform the subtraction if the dimensions match.
3. Conclude with the result or state that the operation is not defined.

STEP 3

First, determine the dimensions of matrices B B and C C .
Matrix B B is a 3×2 3 \times 2 matrix: B=[505553] B = \begin{bmatrix} -5 & 0 \\ 5 & 5 \\ 5 & 3 \end{bmatrix}
Matrix C C is also a 3×2 3 \times 2 matrix: C=[510433] C = \begin{bmatrix} 5 & -1 \\ 0 & -4 \\ 3 & -3 \end{bmatrix}
Since both matrices B B and C C have the same dimensions, matrix subtraction is defined.

STEP 4

Subtract matrix C C from matrix B B element-wise:
BC=[550(1)505(4)533(3)] B - C = \begin{bmatrix} -5 - 5 & 0 - (-1) \\ 5 - 0 & 5 - (-4) \\ 5 - 3 & 3 - (-3) \end{bmatrix}
BC=[1015926] B - C = \begin{bmatrix} -10 & 1 \\ 5 & 9 \\ 2 & 6 \end{bmatrix}
The result of the operation BC B - C is:
[1015926] \begin{bmatrix} -10 & 1 \\ 5 & 9 \\ 2 & 6 \end{bmatrix}

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