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A=[[-1],[4],[4]]" and "F=[[0,-2]] Let H=AF. Find H. H=[]

A=[−144] and F=[0−2] A=\left[\begin{array}{r} -1 \\ 4 \\ 4 \end{array}\right] \text { and } \mathrm{F}=\left[\begin{array}{ll} 0 & -2 \end{array}\right] \newlineLet H=AF \mathrm{H}=\mathrm{AF} . Find H \mathrm{H} .\newlineH= \mathbf{H}=

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Full solution

Q. A=[−144] and F=[0−2] A=\left[\begin{array}{r} -1 \\ 4 \\ 4 \end{array}\right] \text { and } \mathrm{F}=\left[\begin{array}{ll} 0 & -2 \end{array}\right] \newlineLet H=AF \mathrm{H}=\mathrm{AF} . Find H \mathrm{H} .\newlineH= \mathbf{H}=
  1. Define Matrices AA and FF: Define the matrices AA and FF.\newlineMatrix AA is given as A=[[−1],[4],[4]]A = [[-1], [4], [4]] which is a 3×13 \times 1 matrix.\newlineMatrix FF is given as F=[[0,−2]]F = [[0, -2]] which is a 1×21 \times 2 matrix.\newlineTo multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, AA has FF11 column and FF has FF11 row, so the multiplication is possible.
  2. Perform Matrix Multiplication: Perform the matrix multiplication H=AFH = AF. To multiply AA by FF, we take each element of AA and multiply it by each element of FF, then sum the products to get the elements of the resulting matrix HH. H=[[−1×0+(−1)×(−2)],[4×0+4×(−2)],[4×0+4×(−2)]]H = [[-1 \times 0 + (-1) \times (-2)], [4 \times 0 + 4 \times (-2)], [4 \times 0 + 4 \times (-2)]] This simplifies to: H=[[2],[−8],[−8]]H = [[2], [-8], [-8]]
  3. Verify Resulting Matrix Dimensions: Verify the dimensions of the resulting matrix HH. After the multiplication, we should have a matrix with the same number of rows as AA and the same number of columns as FF. Since AA is 3×13 \times 1 and FF is 1×21 \times 2, the resulting matrix HH should be 3×23 \times 2.

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