Question

A=2B where A and B are square matrices of order 3*3 and |B|=5,what is |A|

Answer 1

Answer:

|A| = 40

Explanation :

|A| = 2^3 |B|

|A| = 8 × 5 = 40

Answer 2

The value of |A| = 40

Given :

• A = 2B where A and B are square matrices of order 3*3

• |B| = 5

To find :

The value of |A|

Concept :

For a square matrix B order n

$\displaystyle \sf{ |kB| = {k}^{n} |B| }$

Where k is non zero constant

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that A = 2B where A and B are square matrices of order 3*3

|B| = 5

Step 2 of 2 :

Find the value of |A|

We know that for a square matrix B order n

$\displaystyle \sf{ |kB| = {k}^{n} |B| }$

Where k is non zero constant

Now the given matrices A and B are square matrices of order 3*3

Thus we get ,

$\displaystyle \sf | A |$

$\displaystyle \sf = | 2B |$

$\displaystyle \sf = {2}^{3} \times | B |$

$\displaystyle \sf = {2}^{3} \times 5$

$\displaystyle \sf{ = 8 \times 5 }$

$\displaystyle \sf{ = 40 }$

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