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E=[[5],[2],[-2]]" and "D=[[5,3]] Let H=ED. Find H. H=[]

E=[52−2] and D=[53] \mathrm{E}=\left[\begin{array}{r} 5 \\ 2 \\ -2 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{ll} 5 & 3 \end{array}\right] \newlineLet H=ED \mathrm{H}=\mathrm{ED} . Find H \mathrm{H} .\newlineH= \mathbf{H}=

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Full solution

Q. E=[52−2] and D=[53] \mathrm{E}=\left[\begin{array}{r} 5 \\ 2 \\ -2 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{ll} 5 & 3 \end{array}\right] \newlineLet H=ED \mathrm{H}=\mathrm{ED} . Find H \mathrm{H} .\newlineH= \mathbf{H}=
  1. Understand matrix multiplication: Understand matrix multiplication. Matrix multiplication involves taking the rows of the first matrix EE and multiplying them by the columns of the second matrix DD, then summing the products to get the entries of the resulting matrix HH.
  2. Identify matrix dimensions: Identify the dimensions of the matrices.\newlineMatrix EE has dimensions 3×13 \times 1 (33 rows and 11 column), and matrix DD has dimensions 1×21 \times 2 (11 row and 22 columns). The resulting matrix HH will have dimensions that are the product of the number of rows of EE and the number of columns of DD, which is 3×13 \times 111.
  3. Perform matrix multiplication: Perform the matrix multiplication.\newlineWe multiply each element of the rows of EE by the corresponding elements of the columns of DD and sum the products to get the entries of HH.\newlineH=[5×5+(not applicable, as there is only one element in the row and column), 2×5+(not applicable, as there is only one element in the row and column), −2×5+(not applicable, as there is only one element in the row and column)]H = \left[\begin{array}{c} 5 \times 5 + (\text{not applicable, as there is only one element in the row and column}), \ 2 \times 5 + (\text{not applicable, as there is only one element in the row and column}), \ -2 \times 5 + (\text{not applicable, as there is only one element in the row and column}) \end{array}\right]\newlineThis simplifies to:\newlineH=[25, 10, −10]H = \left[\begin{array}{c} 25, \ 10, \ -10 \end{array}\right]

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