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If H = [[1, 2], [2, 4]], what is the rank of H?

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Question: If H = [[1, 2], [2, 4]], what is the rank of H?

Options:

  1. 1
  2. 2
  3. 0
  4. 3

Correct Answer: 1

Solution: 

The rank of H is 1 because the second row is a multiple of the first row.

If H = [[1, 2], [2, 4]], what is the rank of H?

Practice Questions

Q1
If H = [[1, 2], [2, 4]], what is the rank of H?
  1. 1
  2. 2
  3. 0
  4. 3

Questions & Step-by-Step Solutions

If H = [[1, 2], [2, 4]], what is the rank of H?
  • 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.
  • Matrix Rank – The rank of a matrix is the maximum number of linearly independent row or column vectors in the matrix.
  • Linear Dependence – Rows or columns are linearly dependent if one can be expressed as a linear combination of others.
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