Question

Let A = $\left[\begin{array}{ccc}0&1\\5&-1\\\end{array}\right]$ and B = $\left[\begin{array}{ccc}1&-3\\0&-2\\\end{array}\right]$ and C = $\left[\begin{array}{ccc}2&-5\\4&0\\\end{array}\right]$.
Find (3A + 4B - 5C)
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Answer 1

Step-by-step explanation:

Given :-

A = $\pmb{\bf{\left[\begin{array}{ccc}0&1\\5&-1\\\end{array}\right] }}$

B = $\pmb{\bf{\left[\begin{array}{ccc}1&-3\\0&-2\\\end{array}\right] }}$

C = $\pmb{\bf{\left[\begin{array}{ccc}2&-5\\4&0\\\end{array}\right] }}$

To find :-

3A + 4B - 5C

Solution :-

$\Rightarrow \pmb{\bf3{\left[\begin{array}{ccc}0&1\\5&-1\\\end{array}\right] }}$ + $\pmb{\bf4{\left[\begin{array}{ccc}1&-3\\0&-2\\\end{array}\right] }}$ - $\pmb{\bf5{\left[\begin{array}{ccc}2&-5\\4&0\\\end{array}\right] }}$

$\Rightarrow \pmb{\bf{\left[\begin{array}{ccc}0&3\\15&-3\\\end{array}\right] }}$ + $\pmb{\bf{\left[\begin{array}{ccc}4&-12\\0&-8\\\end{array}\right] }}$ - $\pmb{\bf{\left[\begin{array}{ccc}10&-25\\20&0\\\end{array}\right] }}$

$\Rightarrow \pmb{\bf{\left[\begin{array}{ccc}4&-9\\15&-11\\\end{array}\right] }}$ - $\pmb{\bf{\left[\begin{array}{ccc}10&-25\\20&0\\\end{array}\right] }}$

$\Rightarrow \pmb{\bf{\left[\begin{array}{ccc}-6&16\\-5&-11\\\end{array}\right] }}$

∴ The value of 3A + 4B - 5C is $\pmb{\bf{\left[\begin{array}{ccc}-6&16\\-5&-11\\\end{array}\right] }}$.

Answer 2

★Given:-

• $A = \left[\begin{array}{ccc}0&1\\5&-1\\\end{array}\right]$
• $B = \left[\begin{array}{ccc}1&-3\\0&-2\\\end{array}\right]$
• $C = \left[\begin{array}{ccc}2&-5\\4&0\\\end{array}\right]$

★To Find:-

• Find value of 3A + 4B - 5C

★Solution:-

$: { \implies{ \sf{3A + 4B- 5C= 3\left[\begin{array}{ccc}0&1\\5&-1\\\end{array}\right]+4 \left[\begin{array}{ccc}1&-3\\0&-2\\\end{array}\right] - 5 \left[\begin{array}{ccc}2&-5\\4&0\\\end{array}\right]}}}$

$: { \implies{ \sf{3A + 4B- 5C= \left[\begin{array}{ccc}0&3\\15& - 3\\\end{array}\right]+ \left[\begin{array}{ccc}4& - 12\\0& - 8\\\end{array}\right] - \left[\begin{array}{ccc}10&-25\\20&0\\\end{array}\right]}}}$

$: { \implies{ \sf{3A + 4B- 5C= \left[\begin{array}{ccc}0 + 4&3 - 12\\15 + 0& - 3 - 8\\\end{array}\right] - \left[\begin{array}{ccc}10&-25\\20&0\\\end{array}\right]}}}$

$: { \implies{ \sf{3A + 4B- 5C= \left[\begin{array}{ccc}4& - 9\\15 & - 11\\\end{array}\right] - \left[\begin{array}{ccc}10&-25\\20&0\\\end{array}\right]}}}$

$: { \implies{ \sf{3A + 4B- 5C= \left[\begin{array}{ccc}4 - 10& - 9 + 25\\15 - 20& - 11 - 0\\\end{array}\right]}}}$

${ \bf{ : { \implies{ \bf{3A + 4B- 5C= \left[\begin{array}{ccc} - 6& 16\\ - 5& - 11\\\end{array}\right]}}}}}$

${ \bf{{ \therefore{ \bf{3A + 4B- 5C= \left[\begin{array}{ccc} - 6& 16\\ - 5& - 11 \\\end{array}\right]}}}}}$