Matrices

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Step 1: Count the rows. There are 3 rows. Step 2: Count the columns. There are 2 columns. Step 3: Write the order as 3×2. Answer: A is a 3×2 matrix.

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Step 1: Use the rule for total elements in an m×n matrix. Step 2: Total elements = m × n = 3 × 2. Step 3: Multiply. 3 × 2 = 6. Answer: The matrix has 6 elements.

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Step 1: A column matrix has only one column. Step 2: [2,3,6] is written vertically, so it has one column. Step 3: [1 2 3] has one row, so it is a row matrix. Answer: [2,3,6] is a column matrix.

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Step 1: A row matrix has only one row. Step 2: [1 2 3] has one row and three columns. Step 3: [2,3,6] has one column, so it is not a row matrix. Answer: [1 2 3] is a row matrix of order 1×3.

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Step 1: Count rows = 3. Step 2: Count columns = 3. Step 3: A square matrix has equal number of rows and columns. Answer: Yes, it is a square matrix of order 3×3.

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Step 1: A zero matrix has all elements equal to zero. Step 2: [0,0] has both elements zero, so it is a zero matrix. Step 3: [0 1; 0 0] is not a zero matrix because one element is 1. Step 4: [0 0; 0 0]…

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Step 1: I3 means identity matrix of order 3. Step 2: An identity matrix has 1s on the principal diagonal and 0s elsewhere. Step 3: For I3, the order is 3×3. Answer: I3 is a 3×3 identity matrix.

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Use it when adding a matrix and the zero matrix of the same order. Step 1: The zero matrix is the additive identity. Step 2: Adding it does not change the matrix. Example: If A is 2×2, then A + 02×2 =…