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Write a matrix of order 2xx2 in which ev...

Write a matrix of order `2xx2` in which every element is equal to 2 .

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To write a matrix of order 2x2 in which every element is equal to 2, follow these steps: ### Step-by-Step Solution: 1. **Understand the Order of the Matrix**: - A matrix of order 2x2 means it has 2 rows and 2 columns. 2. **Determine the Elements of the Matrix**: - Since every element in the matrix should be equal to 2, we will fill each position in the matrix with the number 2. 3. **Construct the Matrix**: - Write the matrix in the following format: \[ \begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix} \] - Here, the first row contains two elements (2 and 2), and the second row also contains two elements (2 and 2). 4. **Count the Elements**: - Verify that the total number of elements in the matrix is equal to the product of the number of rows and columns: - 2 rows × 2 columns = 4 elements. - Indeed, we have four elements, all of which are 2. 5. **Final Representation**: - The final matrix is: \[ \begin{bmatrix} 2 & 2 \\ 2 & 2 \end{bmatrix} \] - And we can state that the order of the matrix is 2x2.
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Knowledge Check

  • Let a be a matrix of order 2xx2 such that A^(2)=O . tr (A) is equal to

    A
    `1`
    B
    `0`
    C
    `-1`
    D
    none of these
  • construst a matrix of order 2 xx 2 whose elements are defined as a_(ij)=i+3j.

    A
    `A= [{:(-4" " 7),(-5" " 8):}].`
    B
    `A= [{:(4" " -7),(5" " -8):}].`
    C
    `A= [{:(4" " 7),(5" " 8):}].`
    D
    `A= [{:(4" " - 7),(5" " 8):}].`
  • If A is an invertible matrix of order 2, then det (A^(-1)) is equal to

    A
    det(A)
    B
    `(1)/(det(A))`
    C
    1
    D
    0
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