Use the Appropriate Property of Determinants from This Section to Justify

question 89

Short Answer

Use the appropriate property of determinants from this section to justify the true statement. $$\left| \begin{array} { c c c } 1 & 4 & 6 \\- 2 & 7 & 8 \\- 4 & - 1 & 2\end{array} \right| = \left| \begin{array} { c c c } 1 & 4 & 6 \\- 2 & 7 & 8 \\0 & 15 & 26\end{array} \right|$$ Do not evaluate the determinants. Property number 1: If any row (or column) of a square matrix A contains only zeros, then | A | = 0. Property number 2: If square matrix B is obtained from square matrix A by interchanging two rows (or two columns), then | B | = $-$ | A |. Property number 3: If square matrix B is obtained from square matrix A by multiplying each element of any row (or column) of A by some real number k , then | B | = k | A |. Property number 4: If square matrix B is obtained from square matrix A by adding k times a row (or column) of A to another row (or column) of A , then | B | = | A |. Property number 5: If two rows (or columns) of a square matrix A are identical, then | A | = 0. Enter property number only.

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Definitions:

Manual Dexterity

The skill and ability to use one's hands to perform complex tasks with precision and coordination.

Gross Motor Skill Development

The progression of physical abilities that involve large muscle groups, such as walking, jumping, and throwing.

Fine Motor Skills

The ability to coordinate small muscles for tasks requiring precision, such as writing or buttoning a shirt.

Sensorimotor Knowledge

Knowledge acquired through sensory experiences and motor actions, fundamental in early childhood development for understanding the world.