Short answers, pulled from the story.
The word algebra comes from the Arabic term al-jabr, which originally referred to the surgical treatment of bonesetting. It entered the English language in the 16th century from Italian, Spanish, and medieval Latin.
Muhammad ibn Musa al-Khwarizmi wrote The Compendious Book on Calculation by Completion and Balancing in the 9th century. This work was translated into Latin as Liber Algebrae and established the method for transforming equations.
Diophantus provided a detailed treatment of how to solve algebraic equations in Arithmetica during the 3rd century CE. He was the first to experiment with symbolic notation to express polynomials.
Italian polymath Gerolamo Cardano published his book Ars Magna in 1545. It covered many topics in algebra and discussed imaginary numbers while presenting general methods for solving cubic and quartic equations.
An equation is linear if it can be expressed in the form ax + b = c. Linear algebra starts with the study of systems of linear equations using matrices as rectangular arrays of values.