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3 years ago

Evaluate and simplify the expression when c=1 and d=3. 3(2c + d) - 4(c-d) + d2 = [?]

Mathematics

1 answer:

pav-90 [236]3 years ago

5 0

Answer:

<h2>The answer is 32</h2>

Step-by-step explanation:

3( 2c + d) - 4( c - d) + d²

when

c = 1

d = 3

Substitute the values of c and d into the expression and solve

That's

3[ 2(1) + 3 ] - 4( 1 - 3) + 3²

= 3( 2 + 3) - 4( - 2) + 9

= 3(5) + 8 + 9

= 15 + 17

We have the final answer as

Hope this helps you

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A = ???? 4 −2

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Answer:

1. The matrix A isn't the inverse of matrix B.

2. |B|=12, |A|=12

Step-by-step explanation:

1. We want to know if matrix A is the inverse of matrix B, this means that if you do the product between B and A you have to obtain the identity matrix.

We have:

$A=\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]$

and

$B=\left[\begin{array}{cc}3&2\\1&4\end{array}\right]$

A and B are 2×2 matrices (2 rows and 2 columns), if you multiply them you have to obtain a 2×2 matrix.

Then if A is the inverse of B:

$B.A=I$

Where,

$I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

Observation:

If you have two matrices:

$A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]\\and\\B=\left[\begin{array}{cc}e&f\\g&h\end{array}\right]\\\\\\A.B=\left[\begin{array}{cc}(a.e+b.g)&(a.f+b.h)\\(c.e+d.g)&(c.f+d.h)\end{array}\right]$

Now:

$B.A=\left[\begin{array}{cc}3&2\\1&4\end{array}\right].\left[\begin{array}{cc}4&-2\\-1&3\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}4.3+(-2).1&4.2+(-2).4\\(-1).3+3.1&(-1).2+3.4\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}12-2&8-8\\-3+3&-2+12\end{array}\right]\\\\\\B.A=\left[\begin{array}{cc}10&0\\0&10\end{array}\right]$