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If H = [[1, 2], [2, 4]], what is the rank of H?
If H = [[1, 2], [2, 4]], what is the rank of H?
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If H = [[1, 2], [2, 4]], what is the rank of H?
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The rank of H is 1 because the second row is a multiple of the first row.
Questions & Step-by-step Solutions
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Q: If H = [[1, 2], [2, 4]], what is the rank of H?
Solution:
The rank of H is 1 because the second row is a multiple of the first row.
Steps: 6
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Step 1: Understand what the rank of a matrix is. The rank is the maximum number of linearly independent rows or columns in the matrix.
Step 2: Look at the matrix H = [[1, 2], [2, 4]]. It has 2 rows: [1, 2] and [2, 4].
Step 3: Check if the second row [2, 4] is a multiple of the first row [1, 2].
Step 4: Notice that [2, 4] = 2 * [1, 2]. This means the second row is dependent on the first row.
Step 5: Since the second row does not add any new information (it's a multiple of the first), we only have 1 linearly independent row.
Step 6: Therefore, the rank of the matrix H is 1.
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