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D=[[2],[3],[4]]" and "A=[[-2,-2]]
Let 
H=DA. Find 
H.

H=

D=[234] and A=[2amp;2] \mathrm{D}=\left[\begin{array}{l} 2 \\ 3 \\ 4 \end{array}\right] \text { and } \mathrm{A}=\left[\begin{array}{ll} -2 & -2 \end{array}\right] \newlineLet H=DA \mathrm{H}=\mathrm{DA} . Find H \mathrm{H} .\newlineH= \mathbf{H}=

Full solution

Q. D=[234] and A=[22] \mathrm{D}=\left[\begin{array}{l} 2 \\ 3 \\ 4 \end{array}\right] \text { and } \mathrm{A}=\left[\begin{array}{ll} -2 & -2 \end{array}\right] \newlineLet H=DA \mathrm{H}=\mathrm{DA} . Find H \mathrm{H} .\newlineH= \mathbf{H}=
  1. Define Matrices D and A: Define the matrices D and A.\newlineMatrix D is a 3×13 \times 1 matrix and matrix A is a 1×21 \times 2 matrix. The matrices are given as:\newlineD=[2 3 4]D = \left[\begin{array}{c} 2 \ 3 \ 4 \end{array}\right]\newlineA=[2amp;2]A = \left[\begin{array}{cc} -2 & -2 \end{array}\right]
  2. Check Matrix Multiplication: Determine if matrix multiplication is possible.\newlineMatrix multiplication is possible if the number of columns in the first matrix is equal to the number of rows in the second matrix. Since DD is a 3×13 \times 1 matrix and AA is a 1×21 \times 2 matrix, the multiplication is possible.
  3. Perform Matrix Multiplication: Perform the matrix multiplication.\newlineTo multiply DD by AA, we take each element of DD and multiply it by each element of AA, since AA only has one row. The resulting matrix HH will be a 3×23 \times 2 matrix.\newlineH = [[2 \times -2, 2 \times -2],\(\newline [3 \times -2, 3 \times -2],\newline [4 \times -2, 4 \times -2]]\)
  4. Calculate Resulting Matrix HH: Calculate the entries of the resulting matrix HH.H = \begin{bmatrix}-4 & -4\-6 & -6\-8 & -8\end{bmatrix}

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