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B=[[1,4],[1,3]]" and "D=[[4,3],[0,-1]] Let H=BD. Find H. H=[]

B=[1413] and D=[430−1] \mathrm{B}=\left[\begin{array}{ll} 1 & 4 \\ 1 & 3 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{rr} 4 & 3 \\ 0 & -1 \end{array}\right] \newlineLet H=BD \mathrm{H}=\mathrm{BD} . Find H \mathrm{H} .\newlineH= \mathbf{H}=

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Full solution

Q. B=[1413] and D=[430−1] \mathrm{B}=\left[\begin{array}{ll} 1 & 4 \\ 1 & 3 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{rr} 4 & 3 \\ 0 & -1 \end{array}\right] \newlineLet H=BD \mathrm{H}=\mathrm{BD} . Find H \mathrm{H} .\newlineH= \mathbf{H}=
  1. Define Matrices B and D: Define the matrices B and D. Matrix B is given as B=\left[\begin{array}{cc}1 & 4\1 & 3\end{array}\right] and matrix D is given as D=\left[\begin{array}{cc}4 & 3\0 & -1\end{array}\right]. We need to multiply these matrices to find HH.
  2. Recall Matrix Multiplication Rule: Recall the matrix multiplication rule.\newlineTo multiply two matrices, we sum the products of the rows of the first matrix with the corresponding columns of the second matrix.
  3. Calculate First Element of Matrix H: Calculate the first element of matrix H. The first element of H H[1,1]H[1,1] is the sum of the products of the first row of B and the first column of D. H[1,1]=(1×4)+(4×0)=4+0=4H[1,1] = (1 \times 4) + (4 \times 0) = 4 + 0 = 4
  4. Calculate Second Element of First Row: Calculate the second element of the first row of matrix HH. The second element of the first row of HH (H[1,2]H[1,2]) is the sum of the products of the first row of BB and the second column of DD. H[1,2]=(1×3)+(4×−1)=3−4=−1H[1,2] = (1 \times 3) + (4 \times -1) = 3 - 4 = -1
  5. Calculate First Element of Second Row: Calculate the first element of the second row of matrix HH. The first element of the second row of HH (H[2,1]H[2,1]) is the sum of the products of the second row of BB and the first column of DD. H[2,1]=(1×4)+(3×0)=4+0=4H[2,1] = (1 \times 4) + (3 \times 0) = 4 + 0 = 4
  6. Calculate Second Element of Second Row: Calculate the second element of the second row of matrix HH. The second element of the second row of HH (H[2,2]H[2,2]) is the sum of the products of the second row of BB and the second column of DD. H[2,2]=(1×3)+(3×−1)=3−3=0H[2,2] = (1 \times 3) + (3 \times -1) = 3 - 3 = 0
  7. Combine Calculated Elements: Combine the calculated elements to form matrix HH.H=[H[1,1]H[1,2] H[2,1]H[2,2]]H = \left[\begin{array}{cc}H[1,1] & H[1,2]\ H[2,1] & H[2,2]\end{array}\right]H=[4−1 40]H = \left[\begin{array}{cc}4 & -1\ 4 & 0\end{array}\right]

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