Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0001 360720 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.1055 1210856 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.1055 1210856 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1819 4043960 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1833 4071520 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1842 4089232 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1842 4106240 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1850 4113976 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1850 4113976 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.2317 4341944 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2333 4359344 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2339 4380272 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.3372 9466144 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.3374 9466592 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.3374 9466592 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.3376 9474840 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.3379 9476536 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.3387 9509816 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.3387 9510216 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.3388 9510296 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274

When Can Matrices Be Multiplied

It is not always the case that matrices can be multpiled. Matrices A and B can only be multipled if rows and columns match up so that if we are to find the product AB, the number of columns of A is equal to the number of rows of B.

More concisely, we can say a matrix is an r by c matrix if it has r rows and c columns.

If matrix A is an m by n matrix and matrix B is an p by q matrix then AB exists if and only n=p. The product AB is an m by q matrix.

Example:and

A is a 2 by 3 matrix and B is a 4 by 2 matrix. Since 3 neq 4 the product AB does not exist.

Example:and

A is a 2 by 3 matrix and B is a 3 by 2 matrix. Since 3 =3 the product AB exists and will be a 2 by 2 matrix.

Add comment

Security code
Refresh