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calculer ABTAB^T quand A=(−10 32);B=(4−3 02 10)A = \begin{pmatrix} -1 & 0 \ 3 & 2 \end{pmatrix} ;B = \begin{pmatrix} 4 & -3 \ 0 & 2 \ 1 & 0 \end{pmatrix}

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Q. calculer ABTAB^T quand A=(−10 32);B=(4−3 02 10)A = \begin{pmatrix} -1 & 0 \ 3 & 2 \end{pmatrix} ;B = \begin{pmatrix} 4 & -3 \ 0 & 2 \ 1 & 0 \end{pmatrix}
  1. Write Matrices A and B: Step 11: Write down matrix AA and matrix BB.A=(−10 32)A = \begin{pmatrix} -1 & 0 \ 3 & 2 \end{pmatrix}B=(4−3 02 10)B = \begin{pmatrix} 4 & -3 \ 0 & 2 \ 1 & 0 \end{pmatrix}
  2. Calculate Transpose of B: Step 22: Calculate the transpose of matrix BB (BTB^T).\newlineBT=(401 −320)B^T = \begin{pmatrix} 4 & 0 & 1 \ -3 & 2 & 0 \end{pmatrix}
  3. Multiply AA by BTB^T: Step 33: Multiply matrix AA by BTB^T. To multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. AA is 2×22 \times 2 and BTB^T is 2×32 \times 3, so we can multiply AA by BTB^T.

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