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Compute : ["1 2 3 4"][(1),(2),(...

Compute : `["1 2 3 4"][(1),(2),(3),(4)]`.

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To compute the multiplication of the two matrices given in the question, we will follow these steps: ### Step 1: Identify the matrices and their orders The first matrix is: \[ A = \begin{bmatrix} 1 & 2 & 3 & 4 \end{bmatrix} \] This matrix has 1 row and 4 columns, so its order is \(1 \times 4\). The second matrix is: \[ B = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix} \] This matrix has 4 rows and 1 column, so its order is \(4 \times 1\). ### Step 2: Determine the order of the resultant matrix When multiplying matrices, the order of the resultant matrix is determined by the number of rows from the first matrix and the number of columns from the second matrix. Therefore, the order of the resultant matrix \(C\) will be: \[ C = A \times B \quad \text{(order is } 1 \times 1\text{)} \] ### Step 3: Perform the multiplication To compute the element of the resultant matrix \(C\), we multiply the elements of the first matrix \(A\) with the corresponding elements of the second matrix \(B\) and sum them up: \[ C = 1 \times 1 + 2 \times 2 + 3 \times 3 + 4 \times 4 \] Calculating each term: - \(1 \times 1 = 1\) - \(2 \times 2 = 4\) - \(3 \times 3 = 9\) - \(4 \times 4 = 16\) Now, sum these products: \[ C = 1 + 4 + 9 + 16 = 30 \] ### Step 4: Write the resultant matrix The resultant matrix \(C\) is: \[ C = \begin{bmatrix} 30 \end{bmatrix} \] ### Final Answer The result of the multiplication of the two matrices is: \[ \begin{bmatrix} 30 \end{bmatrix} \] ---
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Compute : [(4),(2),(3)]["1 0 2"]

Knowledge Check

  • Compute [(-1,3,0),(2,1,4)]xx[(1,3),(0,2),(-2,-1)]

    A
    `[(1,3),(6,-4)]`
    B
    `[(-1,-3),(6,4)]`
    C
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    D
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    A
    `3 (40)/(113)`
    B
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    D
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