What is the determinant of the matrix \( \begin{pmatrix} 1 & 1 \\ 1 & 1
Practice Questions
Q1
What is the determinant of the matrix \( \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \)?
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Questions & Step-by-Step Solutions
What is the determinant of the matrix \( \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \)?
Step 1: Identify the matrix. The matrix is given as \( \begin{pmatrix} 1 & 1 \\ 1 & 1 \end{pmatrix} \).
Step 2: Write down the formula for the determinant of a 2x2 matrix. The formula is: \( \text{det}(A) = ad - bc \), where the matrix is \( \begin{pmatrix} a & b \\ c & d \end{pmatrix} \).
Step 3: Assign the values from the matrix to the variables in the formula. Here, \( a = 1 \), \( b = 1 \), \( c = 1 \), and \( d = 1 \).
Step 4: Substitute the values into the determinant formula: \( \text{det}(A) = (1)(1) - (1)(1) \).
Step 5: Calculate the first part: \( (1)(1) = 1 \).
Step 6: Calculate the second part: \( (1)(1) = 1 \).
Step 7: Subtract the second part from the first part: \( 1 - 1 = 0 \).
Step 8: Conclude that the determinant of the matrix is 0.
