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{:[F=[[1,2],[-2,3]]" and "],[E=[[0,-1,5],[3,2,1]]]:} Let H=FE. Find H. H=[◻

F=[12−23] and E=[0−15321] \begin{array}{l} F=\left[\begin{array}{rr} 1 & 2 \\ -2 & 3 \end{array}\right] \text { and } \\ \mathrm{E}=\left[\begin{array}{rrr} 0 & -1 & 5 \\ 3 & 2 & 1 \end{array}\right] \\ \end{array} \newlineLet H=FE \mathrm{H}=\mathrm{FE} . Find H \mathrm{H} .\newlineH=[□ \mathbf{H}=[\square

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Full solution

Q. F=[12−23] and E=[0−15321] \begin{array}{l} F=\left[\begin{array}{rr} 1 & 2 \\ -2 & 3 \end{array}\right] \text { and } \\ \mathrm{E}=\left[\begin{array}{rrr} 0 & -1 & 5 \\ 3 & 2 & 1 \end{array}\right] \\ \end{array} \newlineLet H=FE \mathrm{H}=\mathrm{FE} . Find H \mathrm{H} .\newlineH=[□ \mathbf{H}=[\square
  1. Write Matrices F and E: First, let's write down the matrices F and E.\newlineF=[12 −23]F = \begin{bmatrix} 1 & 2 \ -2 & 3 \end{bmatrix}\newlineE=[0−15 321]E = \begin{bmatrix} 0 & -1 & 5 \ 3 & 2 & 1 \end{bmatrix}
  2. Multiply First Row with First Column: Now, we multiply the first row of FF by the first column of EE.(1×0)+(2×3)=0+6=6(1 \times 0) + (2 \times 3) = 0 + 6 = 6
  3. Multiply First Row with Second Column: Next, multiply the first row of FF by the second column of EE.
    (1×−1)+(2×2)=−1+4=3(1\times-1) + (2\times2) = -1 + 4 = 3
  4. Multiply First Row with Third Column: Then, multiply the first row of FF by the third column of EE. (1×5)+(2×1)=5+2=7(1 \times 5) + (2 \times 1) = 5 + 2 = 7
  5. Multiply Second Row with First Column: Now, let's do the second row of FF with the first column of EE.(−2×0)+(3×3)=0+9=9(-2 \times 0) + (3 \times 3) = 0 + 9 = 9
  6. Multiply Second Row with Second Column: Next, the second row of FF with the second column of EE. \newline(−2×−1)+(3×2)=2+6=8(-2 \times -1) + (3 \times 2) = 2 + 6 = 8, but wait, that's not right, it should be −2+6=4-2 + 6 = 4.

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